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Three Archetypical Linear Problems
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LINEAR MATHEMATICS IN INFINITE
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Wavelet Analysis
Contents
Index
Sturm-Liouville Theory
Lecture
18
Subsections
Three Archetypical Linear Problems
The Homogeneous Problem
Sturm-Liouville Systems
Sturm-Liouville Differential Equation
Homogeneous Boundary Conditions
Basic Properties of a Sturm-Liouville Eigenvalue Problem
Orthogonality, Reality, and Uniqueness
Sturm's Comparison Theorem
Phase Analysis of a Linear Second Order O.D.E.
The Prüfer System
Qualitative Results
Phase Analysis of a Sturm-Liouville System
The Boundary Conditions
The Boundary Value Problem
The Behavior of the Phase: The Oscillation Theorem
Discrete Unbounded Sequence of Eigenvalues
Completeness of the Set of Eigenfunctions via Rayleigh's Quotient
Ulrich Gerlach 2010-12-09
