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Equations of mathematical physics [electronic resource] : generalized functions and historical notes / A.S. Demidov.

Demidov, A. S.
2023
QC20 .D46 2023
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Title
Equations of mathematical physics [electronic resource] : generalized functions and historical notes / A.S. Demidov.
Author
Demidov, A. S.
ISBN
9783031303586 (electronic bk.)
303130358X (electronic bk.)
3031303571
9783031303579
DOI
https://doi.org/10.1007/978-3-031-30358-6
Published
Cham : Springer, 2023.
Language
English
Description
1 online resource (260 pages)
Item Number
10.1007/978-3-031-30358-6 doi
Call Number
QC20 .D46 2023
Dewey Decimal Classification
530.15
Summary
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 Poincar--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.
Note
Description based upon print version of record.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed July 12, 2023).
Available in Other Form
Equations of Mathematical Physics
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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.

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