Introduction to the Theory of Distributions by F.G. Friedlander (English) Hardco

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The theory of distributions has acquired a particular importance in the field of linear partial differential equations, as well as having many other applications, for example in harmonic analysis. In this text the theory is taken as far as Schwartz kernels, the Paley-Weiner-Schwartz theorem and Sobolev spaces.

FORMATHardcover LANGUAGEEnglish CONDITIONBrand New Publisher Description

The theory of distributions is an extension of classical analysis which has acquired a particular importance in the field of linear partial differential equations, as well as having many other applications, for example in harmonic analysis. Underlying it is the theory of topological vector spaces, but it is possible to give a systematic presentation without presupposing a knowledge, or using more than a bare minimum, of this. This book adopts this course and is based on graduate lectures given over a number of years. The prerequisites are few, but a reasonable degree of mathematical maturity is expected of the reader, as the treatment is rigorous throughout. From the outset the theory is developed in several variables, unlike most elementary texts; it is taken as far as such important topics as Schwartz kernels, the Paley-Wiener-Schwartz theorem and Sobolev spaces. In this second edition, the notion of the wavefront set of a distribution is introduced, which allows many operations on distributions to be extended to larger classes and gives much more precise understanding of the nature of the singularities of a distribution.This is done in an elementary fashion without using any involved theories. This account should therefore be useful to graduate students and research workers who are interested in the applications of analysis in mathematics and mathematical physics.

Back Cover

This handbook is a fully illustrated compendium of glossary terms and basic principles in the field of palynology, making it an indispensable tool for all palynologists. The general chapter on pollen morphology, anatomy, and pollen development deals with essential aspects of palynology. Where appropriate, ambiguous or poorly recognized aspects are explained in greater detail, based on the present state of knowledge in palynology. The terminology section comprises more than 300 widely used terms illustrated with over 1000 high-quality light and/or electron microscope images. It provides a detailed survey of the manifold ornamentation and structures of pollen walls, and offers insights into their stunning aesthetic beauty. Terms are grouped by context to allow easier and faster comparison of similar features. In general, each term is explained on a page of its own, including the definition, plant species, and, if needed, a comprehensive explanation. The use of the terms in LM, SEM or TEM and their assignment to anatomical, morphological and/or functional pollen features are indicated by icons and color coding, respectively. The textual glossary is arranged alphabetically for faster term searches. Key literature sources are mentioned and select cross-references to the general chapter are included for better comprehension.

Table of Contents

1. Test functions and distributions; 2. Differentiation and multiplication; 3. Distributions and compact support; 4. Tensor products; 5. Convolution; 6. Distribution kernels; 7. Co-ordinate transforms and pullbacks; 8. Fourier transforms; 9. Plancherel's theorem; 10. The Fourier-Laplace transform; Appendix. Topological vector spaces; 11. The calculus of wavefront sets.

Review

'… a very clear, accurate and stimulating version of an important topic, with the emphasis in the right place and with the minimum of fuss.' Review of the first edition in Bulletin of the London Mathematical Society

Promotional

The second edition of a classic graduate text on the theory of distributions.

Promotional "Headline"

The second edition of a classic graduate text on the theory of distributions.

Description for Bookstore

In this classic graduate text, first published in 1999, the theory of distributions is taken as far as such important topics as Schwartz kernels, the Paley-Wiener-Schwartz theorem and Sobolev spaces; and also in this edition, the notion of the wavefront set of a distribution is introduced.

Description for Library

In this classic graduate text, first published in 1999, the theory of distributions is taken as far as such important topics as Schwartz kernels, the Paley-Wiener-Schwartz theorem and Sobolev spaces; and also in this edition, the notion of the wavefront set of a distribution is introduced.

Details ISBN0521640156 Publisher Cambridge University Press Year 1999 Edition 2nd ISBN-10 0521640156 ISBN-13 9780521640152 Format Hardcover Publication Date 1999-01-21 Imprint Cambridge University Press Place of Publication Cambridge Country of Publication United Kingdom Replaces 9780521243001 DEWEY 512.925 Illustrations appendix Author M. Joshi Short Title INTRO TO THE THEORY OF DISTRIB Language English Media Book Birth 1917 Pages 186 DOI 10.1604/9780521640152 UK Release Date 1999-01-21 AU Release Date 1999-01-21 NZ Release Date 1999-01-21 Edition Description 2nd Revised edition Audience Professional & Vocational We've got this

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