Coverart for item
The Resource Application of holomorphic functions in two and higher dimensions, Klaus Gürlebeck, Klaus Habetha, Wolfgang Sprößig, (electronic book)

Application of holomorphic functions in two and higher dimensions, Klaus Gürlebeck, Klaus Habetha, Wolfgang Sprößig, (electronic book)

Label
Application of holomorphic functions in two and higher dimensions
Title
Application of holomorphic functions in two and higher dimensions
Statement of responsibility
Klaus Gürlebeck, Klaus Habetha, Wolfgang Sprößig
Creator
Contributor
Author
Subject
Language
eng
Summary
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 Throughout the book the authors endeavor to present historical references and important personalities.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
Member of
Cataloging source
N$T
http://library.link/vocab/creatorName
Gürlebeck, Klaus
Dewey number
515/.98
Illustrations
illustrations
Index
index present
LC call number
QA331
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1932-
http://library.link/vocab/relatedWorkOrContributorName
  • Habetha, Klaus
  • Sprössig, Wolfgang
http://library.link/vocab/subjectName
Holomorphic functions
Label
Application of holomorphic functions in two and higher dimensions, Klaus Gürlebeck, Klaus Habetha, Wolfgang Sprößig, (electronic book)
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
SPR952108613
Dimensions
unknown
Extent
1 online resource (xv, 390 pages)
File format
unknown
Form of item
online
Isbn
9783034809641
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-0348-0964-1
Other physical details
illustrations (some color)
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
Label
Application of holomorphic functions in two and higher dimensions, Klaus Gürlebeck, Klaus Habetha, Wolfgang Sprößig, (electronic book)
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
SPR952108613
Dimensions
unknown
Extent
1 online resource (xv, 390 pages)
File format
unknown
Form of item
online
Isbn
9783034809641
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-0348-0964-1
Other physical details
illustrations (some color)
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote

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