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Applied Pseudoanalytic Function Theory / by Vladislav V. Kravchenko
(Frontiers in Mathematics. ISSN:16608054)
版 | 1st ed. 2009. |
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出版者 | (Basel : Birkhäuser Basel : Imprint: Birkhäuser) |
出版年 | 2009 |
本文言語 | 英語 |
大きさ | XII, 184 p : online resource |
著者標目 | *Kravchenko, Vladislav V author SpringerLink (Online service) |
件 名 | LCSH:Differential equations LCSH:Mathematical physics LCSH:Operator theory LCSH:Functions of complex variables FREE:Differential Equations FREE:Mathematical Methods in Physics FREE:Operator Theory FREE:Functions of a Complex Variable FREE:Several Complex Variables and Analytic Spaces |
一般注記 | Pseudoanalytic Function Theory and Second-order Elliptic Equations -- Definitions and Results from Bers’ Theory -- Solutions of Second-order Elliptic Equations as Real Components of Complex Pseudoanalytic Functions -- Formal Powers -- Cauchy’s Integral Formula -- Complex Riccati Equation -- Applications to Sturm-Liouville Theory -- A Representation for Solutions of the Sturm-Liouville Equation -- Spectral Problems and Darboux Transformation -- Applications to Real First-order Systems -- Beltrami Fields -- Static Maxwell System in Axially Symmetric Inhomogeneous Media -- Hyperbolic Pseudoanalytic Functions -- Hyperbolic Numbers and Analytic Functions -- Hyperbolic Pseudoanalytic Functions -- Relationship between Hyperbolic Pseudoanalytic Functions and Solutions of the Klein-Gordon Equation -- Bicomplex and Biquaternionic Pseudoanalytic Functions and Applications -- The Dirac Equation -- Complex Second-order Elliptic Equations and Bicomplex Pseudoanalytic Functions -- Multidimensional Second-order Equations 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 HTTP:URL=https://doi.org/10.1007/978-3-0346-0004-0 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783034600040 |
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電子リソース |
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EB00227986 |
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