This book provides a new mathematical theory for the treatment of
an ample series of spatial problems of electrodynamics, particle
physics, quantum mechanics and elasticity theory. This technique
proves to be as powerful for solving the spatial problems of
mathematical physics as complex analysis is for solving planar
problems.
The main analytic tool of the book, a non-harmonic version of
hypercomplex analysis recently developed by the authors, is
presented in detail. There are given applications of this theory to
the boundary value problems of electrodynamics and elasticity
theory as well as to the problem of quark confinement. A new
approach to the linearization of special classes of the
self-duality equation is also considered. Detailed proofs are given
throughout. The book contains an extensive bibliography on closely
related topics.
This book will be of particular interest to academic and
professional specialists and students in mathematics and physics
who are interested in integral representations for partial
differential equations. The book is self-contained and could be
used as a main reference for special course seminars on the
subject.
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