Distributions, Partial Differential Equations, and Harmonic Analysis

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 eithe...

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Bibliographische Detailangaben
1. Verfasser: Mitrea, Dorina (VerfasserIn)
Format: Elektronisch E-Book
Sprache:Englisch
Veröffentlicht: Cham : Springer International Publishing, 2018.
Ausgabe:2nd ed. 2018.
Schriftenreihe:Universitext,
Schlagworte:
Partial differential equations.
Functional analysis.
Fourier analysis.
Potential theory (Mathematics).
ISBN:9783030032968
ISSN:0172-5939
Online-Zugang: Volltext
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Inhaltsangabe:
  • 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. .

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