Distributions, Partial Differential Equations, and Harmonic Analysis. 2nd ed. 2018

種類:

電子ブック

責任表示:

by Dorina Mitrea

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2018

著者名:

• Mitrea, Dorina.
• SpringerLink (Online service)

シリーズ名:

Universitext ;

ISBN:

9783030032968 [3030032965]    

注記:

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. .
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

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