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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)
Resource Information
The item Application of Holomorphic Functions in Two and Higher Dimensions, by Klaus Gürlebeck, Klaus Habetha, Wolfgang Sprößig, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Application of Holomorphic Functions in Two and Higher Dimensions, by Klaus Gürlebeck, Klaus Habetha, Wolfgang Sprößig, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 This book presents applications of hypercomplex analysis to boundary value and initialboundary 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, CauchyFueter, 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 firstorder partial differential equations such as the Maxwell equations, the CarlemanBersVekua system, the Schrödinger equation, and the Beltrami equation. The higherorder equations start with Riccatitype equations. Further topics include spatial fluid flow problems, image and multichannel processing, image diffusion, linear scale invariant filtering, and others. One of the highlights is the derivation of the threedimensional KolosovMushkelishvili 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 Throughout the book the authors endeavor to present historical references and important personalities.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
 Language
 eng
 Extent
 XV, 390 p. 7 illus., 3 illus. in color.
 Contents

 1.Basic Properties of Holomorphic Functions
 2.Conformal and Quasiconformal 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 Initialboundary Value Problems
 9.RiemannHilbert Problems
 10.Initial Boundary Value Problems on the Sphere
 11.Fourier Transforms
 Bibliography
 Index
 Isbn
 9783034809641
 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
 Subject

 Functions of a Complex Variable
 Integral transforms
 Functional analysis
 Partial differential equations
 Partial differential equations
 Operational calculus
 Operational calculus
 Functional Analysis
 Integral transforms
 Electronic resources
 Functional Analysis
 Functions of complex variables
 Mathematics
 Functions of complex variables
 Mathematics
 Integral Transforms, Operational Calculus
 Partial Differential Equations
 Functional analysis
 Partial Differential Equations
 Language
 eng
 Summary
 This book presents applications of hypercomplex analysis to boundary value and initialboundary 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, CauchyFueter, 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 firstorder partial differential equations such as the Maxwell equations, the CarlemanBersVekua system, the Schrödinger equation, and the Beltrami equation. The higherorder equations start with Riccatitype equations. Further topics include spatial fluid flow problems, image and multichannel processing, image diffusion, linear scale invariant filtering, and others. One of the highlights is the derivation of the threedimensional KolosovMushkelishvili 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)
 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 Quasiconformal 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 Initialboundary Value Problems  9.RiemannHilbert 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
 10.1007/9783034809641
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783034809641
 Label
 Application of Holomorphic Functions in Two and Higher Dimensions, by Klaus Gürlebeck, Klaus Habetha, Wolfgang Sprößig, (electronic resource)
 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 Quasiconformal 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 Initialboundary Value Problems  9.RiemannHilbert 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
 10.1007/9783034809641
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783034809641
Subject
 Electronic resources
 Functional Analysis
 Functional Analysis
 Functional analysis
 Functional analysis
 Functions of a Complex Variable
 Functions of complex variables
 Functions of complex variables
 Integral Transforms, Operational Calculus
 Integral transforms
 Integral transforms
 Mathematics
 Mathematics
 Operational calculus
 Operational calculus
 Partial Differential Equations
 Partial Differential Equations
 Partial differential equations
 Partial differential equations
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