The Resource Application of Holomorphic Functions in Two and Higher Dimensions, by Klaus Gürlebeck, Klaus Habetha, Wolfgang Sprößig, (electronic resource)

Application of Holomorphic Functions in Two and Higher Dimensions, by Klaus Gürlebeck, Klaus Habetha, Wolfgang Sprößig, (electronic resource)

Label
Application of Holomorphic Functions in Two and Higher Dimensions
Title
Application of Holomorphic Functions in Two and Higher Dimensions
Statement of responsibility
by Klaus Gürlebeck, Klaus Habetha, Wolfgang Sprößig
Creator
Contributor
Author
Provider
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 Throughout the book the authors endeavor to present historical references and important personalities.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
http://library.link/vocab/creatorName
Gürlebeck, Klaus
Image bit depth
0
LC call number
  • QA307
  • QA432
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Habetha, Klaus.
  • Sprößig, Wolfgang.
  • SpringerLink
http://library.link/vocab/subjectName
  • Mathematics
  • Functional analysis
  • Functions of complex variables
  • Integral transforms
  • Operational calculus
  • Partial differential equations
  • Mathematics
  • Integral Transforms, Operational Calculus
  • Functions of a Complex Variable
  • Partial Differential Equations
  • Functional Analysis
Label
Application of Holomorphic Functions in Two and Higher Dimensions, by Klaus Gürlebeck, Klaus Habetha, Wolfgang Sprößig, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
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
Dimensions
unknown
Extent
XV, 390 p. 7 illus., 3 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783034809641
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-0348-0964-1
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-0348-0964-1
Label
Application of Holomorphic Functions in Two and Higher Dimensions, by Klaus Gürlebeck, Klaus Habetha, Wolfgang Sprößig, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
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
Dimensions
unknown
Extent
XV, 390 p. 7 illus., 3 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783034809641
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-0348-0964-1
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-0348-0964-1

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