Hilbert Space, Boundary Value Problems and Orthogonal Polynomials

Allan M. Krall

ISBN 10: 3034894597 / ISBN 13: 9783034894593

Editore: Birkhäuser Basel, Birkhäuser Basel Okt 2012, 2012

Riguardo questo articolo

This item is printed on demand - Print on Demand Titel. Neuware -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 to orthogonal polynomials. In a sense, this is an updating of E. C. Titchmarsh's classic Eigenfunction Expansions. My interest in these areas began in 1960-61, when, as a graduate student, I was introduced by my advisors E. J. McShane and Marvin Rosenblum to the ideas of Hilbert space. The next year I was given a problem by Marvin Rosenblum that involved a differential operator with an 'integral' boundary condition. That same year I attended a class given by the Physics Department in which the lecturer discussed the theory of Schwarz distributions and Titchmarsh's theory of singular Sturm-Liouville boundary value problems. I think a Professor Smith was the in structor, but memory fails. Nonetheless, I am deeply indebted to him, because, as we shall see, these topics are fundamental to what follows. I am also deeply indebted to others. First F. V. Atkinson stands as a giant in the field. W. N. Everitt does likewise. These two were very encouraging to me during my younger (and later) years. They did things 'right.' It was a revelation to read the book and papers by Professor Atkinson and the many fine fundamen tal papers by Professor Everitt. They are held in highest esteem, and are given profound thanks.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 372 pp. Englisch.

Codice articolo 9783034894593

Dati bibliografici

• Titolo: Hilbert Space, Boundary Value Problems and Orthogonal Polynomials
• Editore: Birkhäuser Basel, Birkhäuser Basel Okt 2012
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 3034894597
• ISBN 13: 9783034894593
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 254 L x 178 A x 21 P (millimetri) 254 millimetri di larghezza per 178 millimetri di altezza per 21 millimetri di profondità
• Peso: 699 grammi

Descrizione articolo

Riassunto

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 to orthogonal polynomials. In a sense, this is an updating of E. C. Titchmarsh's classic Eigenfunction Expansions. My interest in these areas began in 1960-61, when, as a graduate student, I was introduced by my advisors E. J. McShane and Marvin Rosenblum to the ideas of Hilbert space. The next year I was given a problem by Marvin Rosenblum that involved a differential operator with an "integral" boundary condition. That same year I attended a class given by the Physics Department in which the lecturer discussed the theory of Schwarz distributions and Titchmarsh's theory of singular Sturm-Liouville boundary value problems. I think a Professor Smith was the in­ structor, but memory fails. Nonetheless, I am deeply indebted to him, because, as we shall see, these topics are fundamental to what follows. I am also deeply indebted to others. First F. V. Atkinson stands as a giant in the field. W. N. Everitt does likewise. These two were very encouraging to me during my younger (and later) years. They did things "right." It was a revelation to read the book and papers by Professor Atkinson and the many fine fundamen­ tal papers by Professor Everitt. They are held in highest esteem, and are given profound thanks.

Contenuti

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.