Authors: Plaksa S.A., Shpakivskyi V.S.

Summary: This monograph develops a theory of continuous and differentiable in the sense of Gateaux functions called monogenic 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 imensional commutative algebra with two-dimensional radical, finite-dimensional commutative associative algebras, infinitedimensional vector spaces associated with the three-dimensional Laplace equation and infinitedimensional 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.

Reading audience: Graduate students and researchers alike benefit from this book.

ISBN 978-3-031-32256-3 (print) ; 978-3-031-32254-9 (оnline)

DOI: https://doi.org/10.1007/978-3-031-32254-9

Responsible institutions: Institute of Mathematics of the NAS of Ukraine

Published: Cham : Birkhäuser

Size in pages: 550