## Index

Abel's theorem
Orthogonality, Reality, and Uniqueness
application of
Orthogonality, Reality, and Uniqueness
Adjoint Boundary Conditions to Adjoint Boundary Conditions | 3. Apply Green's Identity
for a second order operator
Second Order Operator and
adjoint boundary value problem in 2 dimensions
3. Apply Green's Identity
The Simple String and
The Adjoint of an | The Simple String and | 2. Determine Green's Identity
Hyperbolic Equations
algorithm
pyramid
The Pyramid Algorithm to The Pyramid Algorithm
antilinear
Inner Product Spaces
appriximation via subspaces
Approximation via Subspaces: Analysis to Approximation via Subspaces: Analysis
Aristotle
Preface
auto correlation function
The Fourier Transform as | The Fourier Transform as
Ayn Rand
Boundary Value Problems in
Banach space
Cauchy Completeness: Complete Metric to Cauchy Completeness: Complete Metric
basis
optimal
Chirped Signals and the
beauty of mathematics
Preface
Bessel function
of order zero
3. Apply Green's Identity
Bessel functions
orthonormalized
Orthogonality, Reality, and Uniqueness
Bessel's inequality
Approximation via Subspaces: Analysis | Approximation via Subspaces: Analysis | Approximation via Subspaces: Analysis
bilinear concomitant
Second Order Operator and
vectorial
2. Determine Green's Identity
Bloch's theorem
Fourier Theory
Born approximation
One-dimensional Scattering Problem: Exterior
Born series
One-dimensional Scattering Problem: Exterior
boundary conditions
Cauchy
in two dimentions
Boundary Conditions of a
compatibility between
Second Order Operator and
Dirichlet
in one dimension
The Homogeneous Problem
in two dimentions
Boundary Conditions of a
homogeneous
Homogeneous Boundary Conditions to Homogeneous Boundary Conditions
in two dimensions
Boundary Conditions of a to Boundary Conditions of a
mixed Dirichlet and Neuman
The Homogeneous Problem
mixed Dirichlet and Neumann
Construction of the Green's
Neumann
in one dimension
The Homogeneous Problem
in two dimentions
Boundary Conditions of a
periodic
The Homogeneous Problem
phase formulation of
The Boundary Conditions to The Boundary Conditions
three important types of
Boundary Conditions of a
boundary value problem
for a cavity
Finite Interior Boundary Value to Finite Interior Boundary Value
exterior
One-dimensional Scattering Problem: Exterior | Exterior Boundary Value Problem: to Exterior Boundary Value Problem:
via Green's function
Boundary Value Problem via
homogeneous
The Homogeneous Problem
inhomogeneous
The Totally Inhomogeneous Boundary
via integral equation
Boundary Value Problem via
interior
One-dimensional Cavity Problem: Interior
interior and finite
Finite Interior Boundary Value to Finite Interior Boundary Value
interior and infinite
Infinite Interior Boundary Value to Infinite Interior Boundary Value
branch cut
Review: Branches, Branch Cuts, to Review: Branches, Branch Cuts,
coalescence of poles
Coalescence of Poles into
integration around
Contour Integration Around the
branch of a function
Review: Branches, Branch Cuts, to Review: Branches, Branch Cuts,
Cauchy completeness
Cauchy Completeness: Complete Metric to Cauchy Completeness: Complete Metric
Cauchy completion
of an inner product spacef
Cauchy Completeness: Complete Metric
of a normed linear space
Cauchy Completeness: Complete Metric
of the rationals
Cauchy Completeness: Complete Metric
Cauchy conditions
see initial value conditions
Cauchy data
see initial value data
Cauchy incomplete
Cauchy Completeness: Complete Metric
Cauchy sequence
Cauchy Sequence to Cauchy Sequence
Cauchy-Schwarz inequality
Inner Product Spaces
central approximation space
Central Approximation Space | Unit-Economy via the Two | Unit-Economy via the Two
central space
see central approximation space
characteristic coordinates
Hyperbolic Equations
characteristics
discontinuity across
Hyperbolic Equations | Hyperbolic Equations
characteristics of a hyperbolic equation
Hyperbolic Equations
Chebyshev distance
Normed Linear Spaces
chirped signals
Chirped Signals and the
commuting operators
complete set of
Special Function Theory | Complete Set of Commuting | Complete Set of Commuting to Complete Set of Commuting | Factorization Method for Solving
compatibility condition between boundary conditions
Second Order Operator and
complete metric space
Complete Metric Spaces to Cauchy Completeness: Complete Metric
complete set
Recapitulation
complete set of commuting operators
Complete Set of Commuting to Complete Set of Commuting
complete set of orthonormal functions
Recapitulation
completeness
Completeness
criterion for
Completeness via Green's function
completeness of a set of S-L eigenfunctions
Completeness of the Set to Completeness of the Set | Completeness
completeness relation
Approximation via Subspaces: Analysis | Recapitulation | Isomorphic Hilbert Spaces | Four Properties | Phase Space Representation | Completeness
completeness via Green's function
Completeness via Green's function | Completeness
complexity of mathematics
Preface
conjunct
Second Order Operator and
convolution
Efficient Calculation: Fourier Transform
applied to a translation invariant system
Translation Invariant Systems
critical frequency
Infinite Interior Boundary Value
cross correlation function
The Fourier Transform as
cylinder harmonic
as a superposition of plane waves
Wanted: Rotation Invariant Solutions | Properties of Hankel and
cylinder waves
see cylinder harmonics
cylindrical cavity
wave equation for a
Finite Interior Boundary Value to Finite Interior Boundary Value
degenerate eigenvalue
Special Function Theory | Degenerate Eigenvalues
degrees of freedom
Orthogonality, Reality, and Uniqueness
differential equation
key principle for solving
The Homogeneous Problem
for Prüfer's phase
The Prüfer System
for Prüfer's amplitude
The Prüfer System
qualitative behaviour of its solutions
Qualitative Results to Qualitative Results
second solution to
Orthogonality, Reality, and Uniqueness
dipole
field
Static Multipole Field
moment
Static Multipole Field
Dirac delta function
The Dirac Delta Function to The Dirac Delta Function
Dirichelet basis
Dirichelet kernel of half-integral order
The Dirichlet Kernel
Dirichelet kernel of integral order
The Dirichlet Kernel
Dirichlet kernel
The Dirichlet Kernel
its basic properties
Basic Properties
distance
Chebyshev
Normed Linear Spaces
Hamming
Normed Linear Spaces
Pythagorean
Normed Linear Spaces
distance function
Normed Linear Spaces | Normed Linear Spaces | Normed Linear Spaces | Metric Spaces | Metric Spaces | Metric Spaces
domain of dependence
Hyperbolic Equations
doubly degenerate eigenvalues
Orthogonality, Reality, and Uniqueness
dual basis
Duality Principle
duality relationship
effectiveness of mathematics
Preface
eigenfunctions
via an integral equation
Eigenfunctions via Integral Equations
even and odd
Orthogonality, Reality, and Uniqueness
normalization of
Orthogonality, Reality, and Uniqueness
unique
Orthogonality, Reality, and Uniqueness
uniqueness of
Orthogonality, Reality, and Uniqueness
eigenvalues
discrete and unbounded sequence of
Discrete Unbounded Sequence of to Discrete Unbounded Sequence of
doubly degenerate
Orthogonality, Reality, and Uniqueness
nondegenerate
Orthogonality, Reality, and Uniqueness
simple
Orthogonality, Reality, and Uniqueness
error vector
Approximation via Subspaces: Analysis
Euclidean plane
Helmholtz equation in the
The Helmholtz Equation to Wanted: Rotation Invariant Solutions
rotations in the
Translations and Rotations in | Translations and Rotations in to Translations and Rotations in
symmetry transformations of the
Translations and Rotations in
translations in the
Translations and Rotations in | Translations and Rotations in to Translations and Rotations in
evanescent wave
Infinite Interior Boundary Value
exterior boundary value problem
One-dimensional Scattering Problem: Exterior
factorization method
applied to Laplacian on a two-sphere
Factorization Method for Solving to Factorization Method for Solving
applied to Laplacian on the Euclidean plane
Properties of Hankel and to Properties of Hankel and
for solving Helmholtz's equation on a two-sphere
Factorization Method for Solving to Factorization Method for Solving
for solving Helmholtz's equation on the Euclidean plane
Properties of Hankel and to Properties of Hankel and
father wavelet
see scaling function
filter function
Translation Invariant Systems
first Born approximation
One-dimensional Scattering Problem: Exterior
Fischer, Ernst
The Riesz-Fischer Theorem
Floquet's theorem
Fourier Theory
Fourier integral
The Fourier Integral to Efficient Calculation: Fourier Transform
Fourier integral theorem
The Fourier Integral Theorem
Fourier series
Fourier Series of a
Fourier series theorem
Fourier Series of a
Fourier sine theorem
Fourier Sine Theorem
Fourier theory
Fourier Theory to Wavelet Analysis
Fourier transform
basic properties of
Fourier Transform via Parseval's
via convolution
Efficient Calculation: Fourier Transform
eigenfunctions of the
Orthogonality, Reality, and Uniqueness
eigenvalues of the
The Fourier Transform as
of generalized functions
Fourier Transform via Parseval's
as an isomorphism
The Fourier Transform as
of light from a mode-locked laser
Efficient Calculation: Fourier Transform
of an optical pulse train
Efficient Calculation: Fourier Transform | Efficient Calculation: Fourier Transform
via Parceval's relation
Fourier Transform via Parseval's to Fourier Transform via Parseval's
of a periodic function
Fourier Transform via Parseval's
of a periodic train of Gaussians
Efficient Calculation: Fourier Transform
its robustness
Fourier Transform via Parseval's
of a ticking clock
Fourier Transform via Parseval's
and tranlation invariance
The Fourier Integral
and translation invariant systems
Translation Invariant Systems
as a unitary transformation in
The Fourier Transform as
windowed
Isomorphic Hilbert Spaces
Fourier-Bessel series
Orthogonality, Reality, and Uniqueness
Fraunhofer approximation
Solution to Wave Equation | Solution to Wave Equation
Fraunhofer-Kirchhoff theorem
Solution to Wave Equation
Fredholm alternative
Properties and Utility of
Fresnel approximation
Solution to Wave Equation
Fundamental theorem for Green's functions
Properties and Utility of
Gaussians
periodic train of
Efficient Calculation: Fourier Transform
generating functions
Properties of Hankel and
Green's function
acausal
Unit Impulse Response: General
Green's Function and Its to Green's Function and Its
Unit Impulse Response: General
for the Bessel operator
The Simple String and
causal
Unit Impulse Response: General
construction of
Construction of the Green's to Construction of the Green's | Green's Function
continuity condition for the 1-dimensional
Point Force Applied to
for a vibrating string
String with Free Ends:
formula for a
Construction of the Green's
fundamental theorem for a
Properties and Utility of
for general homogeneous boundary conditions
Unit Impulse Response: General
initial conditions for
Unit Impulse Response: General | Unit Impulse Response: General
jump condition for the 1-dimensional
Point Force Applied to
pictorial definition
Pictorial Definition of a to Point Force Applied to
poles of a
Spectral Representation
properties and utility
Properties and Utility of to Properties and Utility of
reciprocity relation
Green's Function and Its
retarded
Unit Impulse Response: General
Green's Function and Its
spectral representation
Spectral Representation to Completeness
spectrum via
Spectrum via Green's Function
for a static string
Construction of the Green's
for a translation invariant system
Translation Invariant Systems
uniqueness of
Properties and Utility of
Green's function problem
Introduction
Green's function theory
Green's Function Theory to Fourier Sine Theorem
Green's identity
adapted to a given differential operator in 2 dimensions
2. Determine Green's Identity
in one dimension
Orthogonality, Reality, and Uniqueness
in three dimension
Orthogonality, Reality, and Uniqueness
Hamming distance
Normed Linear Spaces
Hankel functions
applications of
Exterior Boundary Value Problem: to Infinite Interior Boundary Value
properties of
Properties of Hankel and to Properties of Hankel and | More Properties of Hankel to More Properties of Hankel
heat conduction in 1 dimension
temperature profile for
Homogeneous Boundary Conditions
Helmholtz equation
The Helmholtz Equation to Wanted: Rotation Invariant Solutions
solution to, in three dimensions
Solution to Wave Equation
in three dimensions
Solution to Wave Equation
Hermetian operator
Hermite-Gauss polynomials
Orthogonality, Reality, and Uniqueness
Hilbert space
Cauchy Completeness: Complete Metric to Cauchy Completeness: Complete Metric
of square integrable functions
Two Prototypical Examples
of square summable sequences
Two Prototypical Examples
hyperbolic differential equation
Hyperbolic Equations to 3. Apply Green's Identity
integration via Riemann's method
Riemann's Method for Integrating to 3. Apply Green's Identity
infinite dimensional vector spaces
Infinite Dimensional Vector Spaces to Isomorphic Hilbert Spaces
infinite string
Infinite String to Infinite String
as the limit of a finite string
Infinite String as the to Infinite String as the
initial value conditions
Boundary Conditions of a
initial value data
Boundary Conditions of a | Hyperbolic Equations | 3. Apply Green's Identity
initial value problem
3. Apply Green's Identity
inner product norm
Normed Linear Spaces
inner product space
Inner Product Spaces
integral equation
One-dimensional Scattering Problem: Exterior
eigenfunctions via
Eigenfunctions via Integral Equations
integral equations
Boundary Value Problem via to Types of Integral Equations
of the first kind
Types of Integral Equations | Types of Integral Equations
Fredholm -
Types of Integral Equations
of the second kind
Types of Integral Equations | Types of Integral Equations
types of
Types of Integral Equations to Types of Integral Equations
Volterra -
Types of Integral Equations
interior boundary value problem
One-dimensional Cavity Problem: Interior
invariant subspace
Complete Set of Commuting
isometric transformation
Isomorphic Hilbert Spaces
isometry
Isomorphic Hilbert Spaces | The Fourier Transform as
isomorphic Hilbert spaces
Isomorphic Hilbert Spaces to Isomorphic Hilbert Spaces
isomorphism
Isomorphic Hilbert Spaces
Klein-Gordon wave equation
3. Apply Green's Identity
Lagrange's identity
Orthogonality, Reality, and Uniqueness | Orthogonality, Reality, and Uniqueness | Sturm's Comparison Theorem | 2. Determine Green's Identity
extension to two-dimensional domain
2. Determine Green's Identity
laser
mode-locked
Efficient Calculation: Fourier Transform
phase-locked
Efficient Calculation: Fourier Transform
least squares approximation
Approximation via Subspaces: Analysis | The Dirichlet Kernel
Legendre polynomials
orthogonality of
Orthogonality, Reality, and Uniqueness
Legendre's equation
Factorization Method for Solving | The Bessel-Legendre Connection
its relation to Bessel's equation
The Bessel-Legendre Connection
light bullets''
Efficient Calculation: Fourier Transform
linear algebra
archetypical problems
Introduction
logic
father of
Preface
lowering operator
Properties of Hankel and | Factorization Method for Solving
magnetic dipole moment
Electromagnetic Fields in a
magnetic moment density
Electromagnetic Fields in a
magnetization
see magnetic moment density
Mallat, Stephane G.
Fourier Series of a | The Pyramid Algorithm
matched filter
The Fourier Transform as
mathematics
Preface
as neither intrinsic nor subjective
Preface
basis of
Preface
beauty of
Preface
definition of
Preface
effectiveness of
Preface
its complexity
Preface
nature of
Preface to Preface
power of
Preface
theoretical vs. pure''
Preface
Maxwell's equations
System of Partial Differential
how to solve them
System of Partial Differential to The TEM Field
in cylindrical coordinates
The TE Field to The TEM Field
mean frequency
Four Properties
mean position
Four Properties
mean squared error
Approximation via Subspaces: Analysis
metric space
Metric Spaces to Metric Spaces
complete
Complete Metric Spaces to Cauchy Completeness: Complete Metric
definition of
Metric Spaces
metric of
Metric Spaces
mode-locked laser
Efficient Calculation: Fourier Transform
moment
dipole
Static Multipole Field
monopole
Static Multipole Field
Static Multipole Field
monopole
field
Static Multipole Field
moment
Static Multipole Field
mother wavelet
Construction and Properties
MRA
see multiresolution analysis
MSA
see multiscale analysis
MSA vs MRA
Multiscale Analysis vs Multiresolution
multiple scattering
One-dimensional Scattering Problem: Exterior
multipole
field
Static Multipole Field
moment
Static Multipole Field
multipole field
Static Multipole Field to Static Multipole Field
multiresolution analysis
Multiresolution Analysis | Unit-Economy via the Two | Multiscale Analysis vs Multiresolution
multiscale analysis
Unit-Economy via the Two | Multiscale Analysis vs Multiresolution
nondegenerate eigenvalues
Orthogonality, Reality, and Uniqueness | Orthogonality, Reality, and Uniqueness
nonessential properties
see essential properties
normal forms
three types of
Cauchy Problem and Characteristics
normal mode
energy residing in each
Orthogonality, Reality, and Uniqueness
spatial amplitude profile for
Sturm-Liouville Differential Equation
normed linear spaces
Normed Linear Spaces
null coordinates
see characteristic coordinates
onto
The Riesz-Fischer Theorem
optical pulse train
Efficient Calculation: Fourier Transform
Fourier transform of
Efficient Calculation: Fourier Transform | Efficient Calculation: Fourier Transform
optimal basis
Chirped Signals and the
orthogonal eigenfunctions
definition
Orthogonality, Reality, and Uniqueness
orthonormal wave packets
Orthonormal Wave Packet Representation to Phase Space Representation
definition and properties
Orthonormal Wave Packets: Definition to Whittaker-Shannon Sampling Theorem: The
Four Properties
general construction
Orthonormal Wave Packets: General to Orthonormal Wave Packets: General
mean frequency
Four Properties
mean position
Four Properties
phase space representation
Phase Space Representation to Phase Space Representation
sifting property
Four Properties
Four Properties
orthonormal wavelet representation
Orthonormal Wavelet Representation to Construction and Properties
orthonormal wavelets
construction and properties
Construction and Properties to Construction and Properties
orthonormality
Orthogonality, Reality, and Uniqueness
as an expression of energy conservation in each normal mode
Orthogonality, Reality, and Uniqueness
oscillation theorem
The Behavior of the to The Behavior of the
outgoing
wave
Exterior Boundary Value Problem:
parity operator
Orthogonality, Reality, and Uniqueness
Parseval's relation
Approximation via Subspaces: Analysis | Recapitulation | Isomorphic Hilbert Spaces
partial differential equations
Single Partial Differential Equations: to 3. Apply Green's Identity
classification of
Cauchy Problem and Characteristics
three types of
Single Partial Differential Equations: | Cauchy Problem and Characteristics
partial Fourier sum
Fourier Series of a
periodic function
as a convolution
Efficient Calculation: Fourier Transform
Fourier transform of
Fourier Transform via Parseval's
phase analysis
Phase Analysis of a to Discrete Unbounded Sequence of
phase space
partitioning of
Phase Space Representation | Central Approximation Space | Central Approximation Space | Resolution Analysis as a | Resolution Analysis as a | Resolution Analysis as a | Resolution Analysis as a
phase space cells
Phase Space Representation
phase space representation
Phase Space Representation to Phase Space Representation
phase-coherent pulses
Efficient Calculation: Fourier Transform
plane wave
as a superposition of cylinder waves
Properties of Hankel and to Properties of Hankel and
Poincaré phase plane
The Prüfer System | The Prüfer System | The Prüfer System
point transformations
Translations and Rotations in
Poisson's equation
The Simple String and
Poisson's summation formula
Fourier Series of a | Fourier Series of a
alternate form of
Fourier Series of a
positive definite
Inner Product Spaces
power of mathematics
Preface
Prüfer
amplitude
The Prüfer System
phase
The Prüfer System
substitution
The Prüfer System
system
The Prüfer System | The Prüfer System to Qualitative Results
preimage of an element
The Riesz-Fischer Theorem
principle of unit-economy
Chirped Signals and the | Unit-Economy via the Two | Partial Differential Equations
pure'' mathematics as an invalid notion
Preface
pyramid algorithm
The Pyramid Algorithm to The Pyramid Algorithm
Pythagoras' theorem
Approximation via Subspaces: Analysis
Pythagorean distance
Normed Linear Spaces
field
Static Multipole Field
moment
Static Multipole Field
raising operator
Properties of Hankel and | Factorization Method for Solving
Rand, Ayn
Boundary Value Problems in
Rayleigh quotient
Completeness of the Set
reciprocity relation
Green's Function and Its
reconstruction problem
regular S-L problem
Orthogonality, Reality, and Uniqueness | Sturm's Comparison Theorem
resolution analysis
resolution spaces
Resolution Spaces as Hierarchical
resolvent
Spectral Resolution of the
of an operator
Spectral Resolution of the
retarded time
Hyperbolic Equations
Riemann sheets
Review: Branches, Branch Cuts, to Review: Branches, Branch Cuts,
Riemann's method for integrating a hyperbolic equation
Riemann's Method for Integrating to 3. Apply Green's Identity
Riemann's representation of a solution to a hyperbolic equation
3. Apply Green's Identity
Riemann-Lebesgue lemma
Fourier Series of a | Fourier Series of a | The Fourier Integral Theorem
Riesz basis
Central Approximation Space | Unit-Economy via the Two | Unit-Economy via the Two
Riesz, Frigyes
The Riesz-Fischer Theorem
Riesz-Fischer theorem
The Riesz-Fischer Theorem | Subspace Approximation vs. the
rotation eigenfunction
Wanted: Rotation Invariant Solutions
rotation generator
Translations and Rotations in
rotation operator
Translations and Rotations in
scaling equation
The Scaling Function as
scaling function
Central Approximation Space | Resolution Spaces as Hierarchical | The Scaling Function as
scattered wave
Exterior Boundary Value Problem:
scattering
multiple
One-dimensional Scattering Problem: Exterior
scattering problem
Exterior Boundary Value Problem: to Exterior Boundary Value Problem:
scattering process
One-dimensional Scattering Problem: Exterior
Green's function
Green's Function and Its
operator
Shannon basis
Central Approximation Space | Translation Followed by Compression
Shannon's sampling functions
Isomorphic Hilbert Spaces
sifting property
simple string
The Simple String and
sinc function
Phase Space Representation
singular S-L problem
Orthogonality, Reality, and Uniqueness | Sturm's Comparison Theorem
special function theory
Special Function Theory to The Bessel-Legendre Connection
spectral representation
of a Green's function
Spectral Representation to Completeness
of the identity
Recapitulation | Spectral Resolution of the
of a Green's function
Spectral Representation
of the Dirac delta function
Spectral Representation of the
of an operator
Spectral Resolution of the
of a resolvent
Spectral Resolution of the
Spectrum via Green's function
Spectrum via Green's Function
spherical harmonics
Factorization Method for Solving to Factorization Method for Solving
their relation to cylinder harmonics
The Bessel-Legendre Connection to The Bessel-Legendre Connection
spherically symmetric solutions
Spherically Symmetric Solutions to Spherically Symmetric Solutions
spherically symmetric systems, wave equation for
Wave Equation for Spherically to Wave Equation for Spherically
square integrability
Square Integrability to Square Integrability
square integrable functions
Two Prototypical Examples
square summable sequence
Two Prototypical Examples
steepest descent and stationary phase, the method of
The Method of Steepest to The Method of Steepest
string
imbedded in an elastic medium
Sturm-Liouville Differential Equation | 3. Apply Green's Identity
static
Construction of the Green's
with free ends
String with Free Ends: to Completeness
Sturm's comparison theorem
Sturm's Comparison Theorem to Sturm's Comparison Theorem
Sturm-Liouville
differential equation
Sturm-Liouville Differential Equation to Sturm-Liouville Differential Equation
eigenvalue problem
Basic Properties of a to Sturm's Comparison Theorem
periodic
Orthogonality, Reality, and Uniqueness | Orthogonality, Reality, and Uniqueness
reality of its eigenvalues
Orthogonality, Reality, and Uniqueness
regular
Orthogonality, Reality, and Uniqueness | Orthogonality, Reality, and Uniqueness
singular
Orthogonality, Reality, and Uniqueness | Orthogonality, Reality, and Uniqueness
unique solution to
Orthogonality, Reality, and Uniqueness
uniqueness theorem for eigenfunctions
Orthogonality, Reality, and Uniqueness
systems
Sturm-Liouville Systems to Sturm's Comparison Theorem
completeness of their sets of eigenfunctions
Completeness of the Set to Completeness of the Set
meaning of
Basic Properties of a
phase analysis of
Phase Analysis of a to Discrete Unbounded Sequence of
theory
Sturm-Liouville Theory to Completeness of the Set
symmetries
of the Helmholtz equation
Symmetries of the Helmholtz
TE field
The TE Field
TE mode
see TE field
TEM field
The TEM Field
TEM mode
see TEM field
time, definition of
The Prüfer System
TM field
The TM Field
TM mode
see TM field
transfer function
Translation Invariant Systems
translation eigenfunction
Translations and Rotations in
translation generator
Translations and Rotations in | Translations and Rotations in
translation invariant
function space
Unit-Economy via the Two
systems
Translation Invariant Systems
translation operator
Translations and Rotations in
transverse electric magnetic mode
see TEM field
transverse electric mode
see TE field
transverse magnetic mode
see TM field
triangle inequality
Inner Product Spaces | Metric Spaces | Metric Spaces
unit impulse response
see Green's function
unit-economy
Unit-Economy via the Two
principle of
Chirped Signals and the | Unit-Economy via the Two | Partial Differential Equations
unitary transformation between Hilbert spaces
Isomorphic Hilbert Spaces | Orthonormal Wave Packets: General
vibrating cable
Sturm-Liouville Differential Equation
vibrating string
equation
Sturm-Liouville Differential Equation
kinetic energy of
Orthogonality, Reality, and Uniqueness
normal mode for
Sturm-Liouville Differential Equation
potential energy of
Orthogonality, Reality, and Uniqueness
simple
The Homogeneous Problem
total energy of
Orthogonality, Reality, and Uniqueness | Orthogonality, Reality, and Uniqueness
vibrational degree of freedom
energy in each
Orthogonality, Reality, and Uniqueness
vibrations in 1 dimensions
amplitude profile of
Homogeneous Boundary Conditions
wave equation
Sturm-Liouville Differential Equation
for a cylindrical cavity
Finite Interior Boundary Value to Finite Interior Boundary Value
for an imbedded string
3. Apply Green's Identity
Klein-Gordon
3. Apply Green's Identity
spherically symmetric solutions to
Spherically Symmetric Solutions to Spherically Symmetric Solutions
for spherically symmetric systems
Wave Equation for Spherically to Wave Equation for Spherically
static solutions to
Static Solutions to Static Multipole Field
wavelet
analysis
Wavelet Analysis to Wavelet Analysis
generation theorem
Wavelet Analysis
wavelet representation
Orthonormal Wavelet Representation
construction and properties
Construction and Properties
wavepacket representation theorem
Phase Space Representation
Wheeler's motto
Preface
Wheeler, John A.
Preface
Whittaker-Shannon sampling theorem
finite interval version
Whittaker-Shannon Sampling Theorem: The
infinite interval version
Whittaker-Shannon Sampling Theorem: The
Wiener-Khintchine formula
The Fourier Transform as
Wronskian
Orthogonality, Reality, and Uniqueness | Orthogonality, Reality, and Uniqueness
Wronskian determinant
Orthogonality, Reality, and Uniqueness
zeros of a solution
Qualitative Results
are isolated
Qualitative Results

Ulrich Gerlach 2010-12-09