Distributions, Partial Differential Equations, and Harmonic Analysis

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 theory of distributions constitutes an essential tool in the study of partial differential equations. This textbook would offer, in a concise, largely self-contained form, a rapid introduction to the theory of distributions and its applications to partial differential equations, including computing fundamental solutions for the most basic differential operators: the Laplace, heat, wave, Lam'e and Schrodinger operators.

Largely self-contained, rapid introduction to the theory of distributions and its applications to partial differential equations

Contains the computation of fundamental solutions for the Laplacian, heat, wave, Lam'e, Schrodinger, and Cauchy operators

Each chapter contains exercises and many have solutions at the end of the book

Autorentext

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

Inhalt
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.