Distributions, partial differential equations, and harmonic analysis Dorina Mitrea

Format:

Book

Author/Creator:

Mitrea, Dorina, 1965- author.

Series:

Universitext 0172-5939

Language:

English

Subjects (All):

Theory of distributions (Functional analysis).

Differential equations, Partial.

Harmonic analysis.

Fourier Analysis.

Mathematics.

Partial Differential Equations.

Functional Analysis.

Potential Theory.

Medical Subjects:

Fourier Analysis.

Local Subjects:

Mathematics.

Partial Differential Equations.

Functional Analysis.

Fourier Analysis.

Potential Theory.

Physical Description:

1 online resource

Place of Publication:

New York Springer 2013

System Details:

PDF

text file

Summary:

The aim of this book is to offer, in a concise, rigorous, and largely self-contained manner, a rapid introduction to the theory of distributions and its applications to partial differential equations and harmonic analysis. The book is written in a format suitable for a graduate course spanning either over one-semester, when the focus is primarily on the foundational aspects, or over a two-semester period that allows for the proper amount of time to cover all intended applications as well. It presents a balanced treatment of the topics involved, and contains a large number of exercises (upwards of two hundred, more than half of which are accompanied by solutions), which have been carefully chosen to amplify the effect, and substantiate the power and scope, of the theory of distributions. Graduate students, professional mathematicians, and scientifically trained people with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. Throughout, a special effort has been made to develop the theory of distributions not as an abstract edifice but rather give the reader a chance to see the rationale behind various seemingly technical definitions, as well as the opportunity to apply the newly developed tools (in the natural build-up of the theory) to concrete problems in partial differential equations and harmonic analysis, at the earliest opportunity

Contents:

Introduction

Summary of Topological and Functional Analysis Results

Weak Derivatives

The Space D0() of Distributions

The Fourier Transform

The Space of Tempered Distributions

Fundamental Solution

The Laplace Operator

The Heat Operator

The Wave Operator

The Lame Operator

Fundamental Solutions for Other Operators

Hypoelliptic operators

Sobolev spaces

Appendix

References

Weak Derivatives The Space D'(Ω) of Distributions The Schwartz Space and the Fourier Transform The Space of Tempered Distributions The Concept of a Fundamental Solution Hypoelliptic Operators The Laplacian and Related Operators The Heat Operator and Related Versions The Wave Operator The Lamé and Stokes Operators More on Fundamental Solutions for Systems Solutions to Selected Exercises Appendix

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (SpringerLink, viewed September 24, 2013)

Other Format:

Printed edition:

ISBN:

9781461482086

1461482089

1461482070

9781461482079

OCLC:

859773310

Access Restriction:

Restricted for use by site license