عنوان

Distributions, Partial Differential Equations, and Harmonic Analysi

9781461482086

IR

EN-52409

انگلیسی

IR

Distributions, Partial Differential Equations, and Harmonic Analysi

[Book]

:[delta

/ by Dorina Mitrea

New York, NY

: Springer New York :Imprint: Springer,

, 2013.

XXI, 460 p., online resource.

(Universitext,0172-5939)

Electronic

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.

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..?╗╣

Universitext,0172-5939

Mathematics

Fourier analysis

Functional analysis

Differential equations, partial

Potential theory (Mathematics)

Electronic books

Mitrea, Dorina.

SpringerLink (Online service)

ایران

9781461482079.pdf

عادی

عادی

9781461482079.pdf

متن

old catalog

e

BL

1

a

Y