Representations of Linear Operators Between Banach Space
General Material Designation
[Book]
Other Title Information
:[delta
First Statement of Responsibility
/ by David E. Edmunds, W. Desmond Evans
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Basel
Name of Publisher, Distributor, etc.
: Springer Basel :Imprint: Birkh?nuser,
Date of Publication, Distribution, etc.
, 2013.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
XI, 152 p. 1 illus. in color., online resource.
SERIES
Series Title
(Operator Theory
Other Title Information
: Advances and Applications,0255-0156
Volume Designation
; 238)
NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
Text of Note
Electronic
CONTENTS NOTE
Text of Note
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.
Text of Note
1 Preliminaries -- 2 Representation of compact linear operators -- 3 Representation of bounded linear operators.?╗╣
SERIES
Title
Operator Theory: Advances and Applications,0255-0156