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Distributions, Partial Differential Equations, and Harmonic Analysis

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​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.​

Author(s): Dorina Mitrea (auth.)
Series: Universitext
Edition: 1
Publisher: Springer-Verlag New York
Year: 2013

Language: English
Pages: 460
Tags: Partial Differential Equations; Functional Analysis; Fourier Analysis; Potential Theory

Front Matter....Pages i-xxi
Weak Derivatives....Pages 1-16
The Space $$\mathcal{D}^{\prime}(\Omega )$$ of Distributions....Pages 17-87
The Schwartz Space and the Fourier Transform....Pages 89-108
The Space of Tempered Distributions....Pages 109-187
The Concept of a Fundamental Solution....Pages 189-200
Hypoelliptic Operators....Pages 201-216
The Laplacian and Related Operators....Pages 217-275
The Heat Operator and Related Versions....Pages 277-288
The Wave Operator....Pages 289-308
The Lamé and Stokes Operators....Pages 309-339
More on Fundamental Solutions for Systems....Pages 341-374
Solutions to Selected Exercises....Pages 375-414
Appendix....Pages 415-447
Back Matter....Pages 449-460