Representations of linear operators between Banach spaces David E. Edmunds, W. Desmond Evans

Format:

Book

Author/Creator:

Edmunds, D. E. (David Eric), author.

Evans, W. D. (William Desmond), author.

Series:

Operator theory, advances and applications v. 238

Operator theory, advances and applications 0255-0156 v. 238

Language:

English

Subjects (All):

Linear operators.

Banach spaces.

Physical Description:

1 online resource

Place of Publication:

Basel Birkhäuser 2013

Summary:

The book deals with the representation in series form of compact linear operators acting between Banach spaces, and provides an analogue of the classical Hilbert space results of this nature that have their roots in the work of D. Hilbert, F. Riesz and E. Schmidt. The representation involves a recursively obtained sequence of points on the unit sphere of the initial space and a corresponding sequence of positive numbers that correspond to the eigenvectors and eigenvalues of the map in the Hilbert space case. The lack of orthogonality is partially compensated by the systematic use of polar sets. There are applications to the p-Laplacian and similar nonlinear partial differential equations. Preliminary material is presented in the first chapter, the main results being established in Chapter 2. The final chapter is devoted to the problems encountered when trying to represent non-compact maps

Contents:

Preliminaries Representation of compact linear operators Representation of bounded linear operators

Machine generated contents note: 1. Preliminaries

1.1. geometry of Banach spaces

1.2. Bases

1.3. p-trigonometric functions

1.4. Entropy numbers and s-numbers

1.4.1. Fundamentals

1.4.2. Gelfand numbers and widths

2. Representation of Compact Linear Operators

2.1. Compact operators in Hilbert spaces

2.2. Compact operators in Banach spaces

2.2.1. Preliminaries

2.2.2. linear projections Sκ

2.2.3. nonlinear projections Pκ: X [→] Xκ

2.2.4. main convergence theorems

2.2.5. basis for X

2.2.6. Schmidt-type expansion for T

2.3. Applications

2.3.1. p-Laplacian

2.3.2. weighted problem for the p-Laplacian

2.3.3. p-Laplacian problem in Rn

2.3.4. p-biharmonic operator

2.3.5. Sturm-Liouville theory for the p-Laplacian

2.4. Lusternik-Schnirelmann critical levels

2.4.1. Comparison of eigenvalues

2.4.2. Hardy-type operator

2.5. Further consequences of the boundedness of (Sn)neN

3. Representation of Bounded Linear Operators

3.1. integral representation of points of X

3.2. integral representation for T

3.3. Compact operators revisited

Notes:

Includes bibliographical references and indexes

Online resource; title from PDF title page (SpringerLink, viewed September 9, 2013)

Other Format:

Print version Edmunds, D.E. (David Eric). Representations of linear operators between Banach spaces

ISBN:

9783034806428

3034806426

OCLC:

858859085

Access Restriction:

Restricted for use by site license