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.
General
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