CiNii Books - Applied pseudoanalytic function theory

Author(s)

- Kravchenko, Vladislav V

Bibliographic Information

Applied pseudoanalytic function theory

Vladislav V. Kravchenko

（Frontiers in mathematics）

Birkhäuser, c2009

: [pbk.]

Available at / 8 libraries

Osaka University, Main Library

: [pbk.]12200253081

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Science and Technology Library, Kyushu University

: [pbk.]023212009001785

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Library, Research Institute for Mathematical Sciences, Kyoto University数研

: [pbk.]KRA||34||2200010694337

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京都大学理学部数学

: [pbk.]KRA||27.15||01200008973178

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東京工業大学大岡山図書館

: [pbk.]400018979

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東京大学数理科学研究科図書

: [pbk.]FU:Kravchenko:V.V.8010504754

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Kita-Aobayama Library,Tohoku University図

: [pbk.]02090002537

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Tokushima University Library

: [pbk.]413.5||Kr211005342

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Note

Includes bibliographical references (p. [173]-181) and index

Description and Table of Contents

Description

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 Schroedinger, 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.

Table of Contents

Introduction.- I. Pseudoanalytic function theory and second-order elliptic equations.- 1. Definitions and results from Bers' theory.- 2. Second order equations.- 3. Formal powers.- 4. Cauchy's integral formula.- 5. Complex Riccati equation.- II. Applications to Sturm-Liouville theory.- 6. Sturm-Liouville equation.- 7. Spectral problems and Darboux transformation.- III. Applications to real first-order systems.- 8. Beltrami fields.- 9. Static Maxwell system.- IV. Hyperbolic pseudoanalytic functions.- 10. Hyperbolic numbers and analytic functions.- 11. Hyperbolic pseudoanalytic functions.- 12. Klein-Gordon equation.- V. Bicomplex and biquaternionic pseudoanalytic functions and applications.- 13. The Dirac equation.- 14. Complex second order elliptic equations and bicomplex pseudoanalytic functions.- 15. Multidimensional second order equations.- Open problems.- Bibliography.- Index.

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