Hilbert space, boundary value problems, and orthogonal polynomials / Allan M. Krall.
This monograph consists of three parts: - the abstract theory of Hilbert spaces, leading up to the spectral theory of unbounded self-adjoined operators; - the application to linear Hamiltonian systems, giving the details of the spectral resolution; - further applications such as to orthogonal polyno...
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| Online Access: |
Full Text (via Springer) |
|---|---|
| Main Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
Basel ; Boston :
Springer/Birkhauser Verlag,
2002.
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| Series: | Operator theory, advances and applications ;
v. 133. |
| Subjects: |
Table of Contents:
- 1
- I Hilbert Spaces
- II Bounded Linear Operators on a Hilbert Space
- III Unbounded Linear Operators on a Hilbert Space
- 2
- IV Regular Linear Hamiltonian Systems
- V Atkinson's Theory for Singular Hamiltonian Systems of Even Dimension
- VI The Niessen Approach to Singular Hamiltonian Systems
- VII Hinton and Shaw's Extension of Weyl's M Theory to Systems
- VIII Hinton and Shaw's Extension with Two Singular Points
- IX The M Surface
- X The Spectral Resolution for Linear Hamiltonian Systems with One Singular Point
- XI The Spectral Resolution for Linear Hamiltonian Systems with Two Singular Points
- XII Distributions
- 3
- XIII Orthogonal Polynomials
- XIV Orthogonal Polynomials Satisfying Second Order Differential Equations
- XV Orthogonal Polynomials Satisfying Fourth Order Differential Equations
- XVI Orthogonal Polynomials Satisfying Sixth Order Differential Equations
- XVII Orthogonal Polynomials Satisfying Higher Order Differential Equations
- XVIII Differential Operators in Sobolev Spaces
- XIX Examples of Sobolev Differential Operators
- XX The Legendre-Type Polynomials and the Laguerre-Type Polynomials in a Sobolev Spaces
- Closing Remarks.