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Kernel Theorem and Microlocal Analysis

Name: Kernel Theorem and Microlocal Analysis
Brand: VDM Verlag
SKU: 06838583
Price: 17613 HUF
Availability: InStock
Author: Vera Ganglberger
ISBN: 9783639317329

Vera Ganglberger

Language

English

Book Paperback

Libristo code: 06838583

Publishers VDM Verlag, December 2010

This book develops several aspects of the theory of distributions on manifolds. Beginning with a sec... Full description

Libristo code: 06838583

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This book develops several aspects of the theory of distributions on manifolds. Beginning with a section on prerequisites, it shortly outlines the most important concepts needed from the fields of functional analysis, differential geometry and distribution theory, thus enabling students with basic knowledge in these fields to follow the main body of the book. The second chapter then deals with the kernel theorem by Laurent Schwartz, stating that all linear and continuous operators from the space of test functions on one manifold into the space of distributions on another manifold can be given by a kernel distribution on the product space. After proving this theorem, regular and regularising kernel operators are examined as special cases of kernel operators that allow an extension of the kernel map to distribution spaces. The last chapter then moves on to microlocal analysis on manifolds, where first of all an intrinsic, coordinate-invariant definition of the wave front set for distributions on a manifold is developed. Ultimately, the thesis returns to regular kernel operators and investigates their microlocal properties.