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Hilbert space, boundary value problems, and orthogonal polynomials

Author: Allan M Krall
Publisher: Basel ; Boston : Springer/Birkhauser Verlag, 2002.
Series: Operator theory, advances and applications, v. 133.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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 polynomials and Sobolev differential operators. Written in textbook style this up-to-date volume is geared towards graduate  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Krall, Allan M.
Hilbert space, boundary value problems, and orthogonal polynomials.
Basel ; Boston : Springer/Birkhauser Verlag, 2002
(DLC) 2002019356
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Allan M Krall
ISBN: 9783034881555 303488155X 3034894597 9783034894593 9783764367015 3764367016 9780817667016 0817667016
OCLC Number: 847549593
Description: 1 online resource (xii, 352 pages).
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.
Series Title: Operator theory, advances and applications, v. 133.
Responsibility: Allan M. Krall.

Abstract:

The following tract is divided into three parts: Hilbert spaces and their (bounded and unbounded) self-adjoint operators, linear Hamiltonian systemsand their scalar counterparts and their application  Read more...

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