Hilbert Space, boundary value problems and orthogonal polynomials
著者
書誌事項
Hilbert Space, boundary value problems and orthogonal polynomials
（Operator theory : advances and applications, v. 133）
Birkhäuser, c2002
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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 and postgraduate students and researchers interested in boundary value problems of linear differential equations or in orthogonal polynomials.
目次
Hilbert Spaces - Bounded Linear Operators on a Hilbert Space - Unbounded Linear Operators on a Hilbert Space - Regular Linear Hamiltonian Systems - Atkinson's Theory for Singular Hamiltonian Systems of Even Dimensions - The Niessen Approach to Singular Hamiltonian Systems - Hinton and Shaw's Extension of Weyl's M(I) Theory to Systems - Hinton and Shaw's Extension with Two Singular Points - The M(I) Surface - The Spectral Resolution for Linear Hamiltonian Systems with One Singular Point - The Spectral Resolution for Linear Hamiltonian Systems with Two Singular Points - Distributions - Orthogonal Polynomials - Orthogonal Polynomials Satisfying Second Order Differential Equations - Orthogonal Polynomials Satisfying Fourth Order Differential Equations - Orthogonal Polynomials Satisfying Sixth Order Differential Equations - Orthogonal Polynomials Satisfying Higher Order Differential Equations - Differential Operators in Sobolev Spaces - Examples of Sobolev Differential Operators - The Legendre-Type Polynomials and the Laguerre-Type Polynomials in a Sobolev Space
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