Hilbert Space, Boundary Value Problems and Orthogonal Polynomials

by Allan M Krall, A M Krall

Overview

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.

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

Product Details

ISBN-13:	9783764367015
Publisher:	Birkhauser Basel
Publication date:	06/10/2002
Series:	Operator Theory: Advances and Applications Series , #133
Pages:	352
Product dimensions:	6.70(w) x 9.20(h) x 1.00(d)

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.