ENGLISH

Representations of Linear Operators Between Banach Spaces

By David E. Edmunds , W. Desmond Evans (auth.)

Book information

Publisher
Birkhäuser Basel
Year
2013
ISBN
978-3-0348-0641-1, 978-3-0348-0642-8
DOI
10.1007/978-3-0348-0642-8
Language
english
Format
PDF
Filesize
2 MB (1718827 bytes)
Series
Operator Theory: Advances and Applications 238
Edition
1
Pages
152\164
Orientation
yes
Scanned
yes
Time added
2013-09-13 10:25:39
Operator Theory; Partial Differential Equations

Description

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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