Overview
- First presentation in book of pseudoanalytic function theory applied to a variety of models of mathematical physics
- Presents new methods for studying models of mathematical physics
- Clearly written, at the level of an undergraduate student acquainted with complex analysis and basics of differential equations
- Includes supplementary material: sn.pub/extras
Part of the book series: Frontiers in Mathematics (FM)
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Table of contents (16 chapters)
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Front Matter
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Introduction
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Pseudoanalytic Function Theory and Second-order Elliptic Equations
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Front Matter
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Applications to Sturm-Liouville Theory
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Front Matter
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Applications to Real First-order Systems
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Front Matter
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Hyperbolic Pseudoanalytic Functions
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Front Matter
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Bicomplex and Biquaternionic Pseudoanalytic Functions and Applications
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Front Matter
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Keywords
About this book
Pseudoanalytic function theory generalizes and preserves many crucial features of complex analytic function theory. The Cauchy-Riemann system is replaced by a much more general first-order system with variable coefficients which turns out to be closely related to important equations of mathematical physics. This relation supplies powerful tools for studying and solving Schrödinger, Dirac, Maxwell, Klein-Gordon and other equations with the aid of complex-analytic methods.
The book is dedicated to these recent developments in pseudoanalytic function theory and their applications as well as to multidimensional generalizations.
It is directed to undergraduates, graduate students and researchers interested in complex-analytic methods, solution techniques for equations of mathematical physics, partial and ordinary differential equations.
Reviews
From the reviews:
“This book presents a renaissance of Bers’ and Vekua’s theory. It can be recommended to colleagues which are interested in the plane function theory.” (Michael Reissig, Zentralblatt MATH, Vol. 1182, 2010)Authors and Affiliations
Bibliographic Information
Book Title: Applied Pseudoanalytic Function Theory
Authors: Vladislav V. Kravchenko
Series Title: Frontiers in Mathematics
DOI: https://doi.org/10.1007/978-3-0346-0004-0
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Basel 2009
Softcover ISBN: 978-3-0346-0003-3Published: 13 May 2009
eBook ISBN: 978-3-0346-0004-0Published: 21 July 2009
Series ISSN: 1660-8046
Series E-ISSN: 1660-8054
Edition Number: 1
Number of Pages: XII, 184
Topics: Partial Differential Equations, Mathematical Methods in Physics, Operator Theory, Functions of a Complex Variable, Several Complex Variables and Analytic Spaces