Equations of Mathematical Physics | Buch

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Cover: 9783031303579 | Equations of Mathematical Physics | A. S. Demidov | Buch | xv | 2023

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Sprache: Englisch

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Beschreibung

This concise volume presents an overview of equations of mathematical physics and generalized functions. While intended for advanced readers, the accessible introduction and text structure allows beginners to study at their own pace as the material gradually increases in difficulty. The text introduces the concept of generalized Sobolev functions and L. Schwartz distributions briefly in the opening section, gradually approaching a more in-depth study of the ¿generalized¿ differential equation (also known as integral equality). In contrast to the traditional presentation of generalized Sobolev functions and L. Schwartz distributions, this volume derives the topology from two natural requirements (which are equivalent to it). The text applies the same approach to the theory of the canonical Maslov operator. It also features illustrative drawings and helpful supplementary reading in the footnotes concerning historical and bibliographic information related to the subject of the book. Additionally, the book devotes a special chapter to the application of the theory of pseudodifferential operators and Sobolev spaces to the inverse magneto/electroencephalography problem.

Explicit numerically realizable formulas related to the Cauchy problem for elliptic equations (including quasilinear ones) and also to the Poincaré--Steklov operators are presented. The book is completed by three additions, which were written by famous mathematicians Yu. V. Egorov, A. B. Antonevich, and S. N. Samborski.

Zusammenfassung

Theory of pseudodifferential operators & Sobolev spaces to the inverse magneto/electroencephalography problem

Presents derivation of generalized Sobolev functions & L. Schwartz distributions

Suitable for both novice & advanced readers

Inhaltsverzeichnis

Introduction. - Introduction to problems of mathmatical physics.- The spaces D¿, D¿ and D¿. Elements of the distribution theory. - Pseudodifferential operators and Fourier operators. - New approach to the theory of generalized functions (Yu.V. Egorov). - Algebras of mnemonic functions (A. B. Antonevich).- Extensions first-order partial differential operators (S.N. Samborskii). - References-. Index.

Erscheinungsjahr:	2023
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	264
Inhalt:	xv 248 S. 1 s/w Illustr. 2 farbige Illustr. 248 p. 3 illus. 2 illus. in color.
ISBN-13:	9783031303579
ISBN-10:	3031303571
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Demidov, A. S.
Auflage:	1st ed. 2023
Hersteller:	Springer International Publishing Springer International Publishing AG
Maße:	241 x 160 x 20 mm
Von/Mit:	A. S. Demidov
Erscheinungsdatum:	28.06.2023
Gewicht:	0,565 kg

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