Distributions, Partial Differential Equations, and Harmonic Analysis

2013
ISBN: 978-1-4614-8207-9
Verlag: Springer

Buch, Englisch, 460 Seiten, Book, Format (B × H): 155 mm x 235 mm, Gewicht: 7256 g

Reihe: Universitext

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Mitrea, Dorina

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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.

Über Autor(innen)

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