Distributions, Partial Differential Equations, and Harmonic Analysis - Dorina Mitrea

Distributions, Partial Differential Equations, and Harmonic Analysis

(Autor)

Buch | Softcover
XXIII, 600 Seiten
2019 | 2nd ed. 2018
Springer International Publishing (Verlag)
978-3-030-03295-1 (ISBN)
69,54 inkl. MwSt
This book offers a rapid introduction to the theory of distributions and its applications to partial differential equations and harmonic analysis. Each chapter contains exercises and many have solutions at the end of the book.
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-studyguide. 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.
The main additions to the current, second edition, pertain to fundamental solutions (through the inclusion of the Helmholtz operator, the perturbed Dirac operator, and their iterations) and the theory of Sobolev spaces (built systematically from the ground up, exploiting natural connections with the Fourier Analysis developed earlier in the monograph). 

Dorina Mitrea is a Professor at University of Missouri in the Mathematics Department.

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. 

Erscheinungsdatum
Reihe/Serie Universitext
Zusatzinfo XXIII, 600 p. 1 illus.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 943 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Schlagworte Cauchy-Reimann operator • Dirac Operator • distributions • fourier analysis • fundamental solutions • Helmholtz operator • Laplacian • Partial Diffential Equations texbook • Partial differential equations • Potential Theory
ISBN-10 3-030-03295-7 / 3030032957
ISBN-13 978-3-030-03295-1 / 9783030032951
Zustand Neuware
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