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Application of Holomorphic Functions in Two and Higher Dimensions
This book presents applications of hypercomplex analysis to boundary value and initial-boundary value problems from various areas of mathematical physics. Given that quaternion and Clifford analysis offer natural and intelligent ways to enter into higher dimensions, it starts with quaternion and Cli...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Basel :
Springer Basel : Imprint: Birkhäuser,
2016.
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| Edición: | 1st ed. 2016. |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-3-0348-0964-1 | ||
| 003 | DE-He213 | ||
| 005 | 20220114104323.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 160620s2016 sz | s |||| 0|eng d | ||
| 020 | |a 9783034809641 |9 978-3-0348-0964-1 | ||
| 024 | 7 | |a 10.1007/978-3-0348-0964-1 |2 doi | |
| 050 | 4 | |a QA299.6-433 | |
| 072 | 7 | |a PBKL |2 bicssc | |
| 072 | 7 | |a MAT034000 |2 bisacsh | |
| 072 | 7 | |a PBKL |2 thema | |
| 082 | 0 | 4 | |a 515.72 |2 23 |
| 100 | 1 | |a Gürlebeck, Klaus. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Application of Holomorphic Functions in Two and Higher Dimensions |h [electronic resource] / |c by Klaus Gürlebeck, Klaus Habetha, Wolfgang Sprößig. |
| 250 | |a 1st ed. 2016. | ||
| 264 | 1 | |a Basel : |b Springer Basel : |b Imprint: Birkhäuser, |c 2016. | |
| 300 | |a XV, 390 p. 7 illus., 3 illus. in color. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 505 | 0 | |a 1.Basic Properties of Holomorphic Functions -- 2.Conformal and Quasi-conformal Mappings -- 3.Function Theoretic Function spaces -- 4.Operator Calculus -- 5.Decompositions -- 6.Some First Order Systems of Partial Differential Equations -- 7.Boundary Value Problems of Second Order Partial Differential Equations -- 8.Some Initial-boundary Value Problems -- 9.Riemann-Hilbert Problems -- 10.Initial Boundary Value Problems on the Sphere -- 11.Fourier Transforms -- Bibliography -- Index. | |
| 520 | |a This book presents applications of hypercomplex analysis to boundary value and initial-boundary value problems from various areas of mathematical physics. Given that quaternion and Clifford analysis offer natural and intelligent ways to enter into higher dimensions, it starts with quaternion and Clifford versions of complex function theory including series expansions with Appell polynomials, as well as Taylor and Laurent series. Several necessary function spaces are introduced, and an operator calculus based on modifications of the Dirac, Cauchy-Fueter, and Teodorescu operators and different decompositions of quaternion Hilbert spaces are proved. Finally, hypercomplex Fourier transforms are studied in detail. All this is then applied to first-order partial differential equations such as the Maxwell equations, the Carleman-Bers-Vekua system, the Schrödinger equation, and the Beltrami equation. The higher-order equations start with Riccati-type equations. Further topics include spatial fluid flow problems, image and multi-channel processing, image diffusion, linear scale invariant filtering, and others. One of the highlights is the derivation of the three-dimensional Kolosov-Mushkelishvili formulas in linear elasticity. Throughout the book the authors endeavor to present historical references and important personalities. The book is intended for a wide audience in the mathematical and engineering sciences and is accessible to readers with a basic grasp of real, complex, and functional analysis. | ||
| 650 | 0 | |a Mathematical analysis. | |
| 650 | 0 | |a Functions of complex variables. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Functional analysis. | |
| 650 | 1 | 4 | |a Integral Transforms and Operational Calculus. |
| 650 | 2 | 4 | |a Functions of a Complex Variable. |
| 650 | 2 | 4 | |a Differential Equations. |
| 650 | 2 | 4 | |a Functional Analysis. |
| 700 | 1 | |a Habetha, Klaus. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Sprößig, Wolfgang. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783034809627 |
| 776 | 0 | 8 | |i Printed edition: |z 9783034809634 |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-0348-0964-1 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||