Representations of Linear Operators Between Banach Spaces (Operator Theory: Advances and Applications, 238) - Hardcover

Edmunds, David E.; Evans, W. Desmond

 
9783034806411: Representations of Linear Operators Between Banach Spaces (Operator Theory: Advances and Applications, 238)

Synopsis

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.

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From the Back Cover

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.

"About this title" may belong to another edition of this title.

Other Popular Editions of the Same Title

9783034806435: Representations of Linear Operators Between Banach Spaces

Featured Edition

ISBN 10:  3034806434 ISBN 13:  9783034806435
Publisher: Birkhäuser, 2013
Softcover