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Monogenic functions in spaces with commutative multiplication and applications / Sergiy A. Plaksa, Vitalii S. Shpakivskyi.

9783031322549 (electronic bk.)
3031322541 (electronic bk.)
9783031322532

Cham : Birkhäuser, [2023]

©2023

English

1 online resource (xvi, 550 pages) : illustrations (some color).

10.1007/978-3-031-32254-9 doi

QA331

515/.9

This monograph develops a theory of continuous and differentiable functions, called monogenic functions, in the sense of Gateaux functions taking values in some vector spaces with commutative multiplication. The study of these monogenic functions in various commutative algebras leads to a discovery of new ways of solving boundary value problems in mathematical physics. The book consists of six parts: Part I presents some preliminary notions and introduces various concepts of differentiable mappings of vector spaces. Part II - V is devoted to the study of monogenic functions in various spaces with commutative multiplication, namely, three dimensional commutative algebras with two-dimensional radical, finite-dimensional commutative associative algebras, infinite-dimensional vector spaces associated with the three-dimensional Laplace equation and infinite-dimensional vector spaces associated with axial-symmetric potential fields. Part VI presents some boundary value problems for axial-symmetric potential fields and develops effective analytic methods of solving these boundary value problems with various applications in mathematical physics. Graduate students and researchers alike benefit from this book.

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed July 26, 2023).

Frontiers in mathematics. 1660-8054

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