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Abels

Pseudodifferential and Singular Integral Operators

An Introduction with Applications
2011. Buch. X, 232 S.: 10 s/w-Abbildungen. Softcover
De Gruyter ISBN 978-3-11-025030-5
Format (B x L): 17 x 24 cm
Gewicht: 393 g
In englischer Sprache
Das Werk ist Teil der Reihe:
This textbook provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their applications to partial differential equations. In the first chapters, the necessary material on Fourier transformation and distribution theory is presented. Subsequently the basic calculus of pseudodifferential operators on the n-dimensional Euclidean space is developed. In order to present the deep results on regularity questions for partial differential equations, an introduction to the theory of singular integral operators is given - which is of interest for its own. Moreover, to get a wide range of applications, one chapter is devoted to the modern theory of Besov and Bessel potential spaces. In order to demonstrate some fundamental approaches and the power of the theory, several applications to wellposedness and regularity question for elliptic and parabolic equations are presented throughout the book. The basic notation of functional analysis needed in the book is introduced and summarized in the appendix. The text is comprehensible for students of mathematics and physics with a basic education in analysis.

Audience

Students and Lecturers in Mathematics and Physics; Academic Libraries

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Highly motivated by problems arising in various applications Appropriate as a textbook for graduate courses or for independent study Several exercises and summaries of each chapter help beginners to understand the material