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BL
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| Record Number
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862560
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| Title & Author
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Topics in Clifford Analysis : : Special Volume in Honor of Wolfgang Sprößig /\ Swanhild Bernstein, editor.
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| Publication Statement
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Cham :: Springer,, 2019.
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| Series Statement
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Trends in Mathematics Ser.
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| Page. NO
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1 online resource (509 pages)
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| ISBN
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3030238547
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: 9783030238544
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9783030238537
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| Notes
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9.5.2 Shearlets
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| Contents
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Intro; Preface; Contents; Contributors; Part I Clifford Analysis Theories; 1 Cauchy's Formula in Clifford Analysis: An Overview; 1.1 Introduction; 1.2 Hermitian Monogenicity; 1.3 Cauchy Integral Formulae in the Hermitian Context; 1.4 Quaternionic Monogenicity; 1.5 Cauchy Integral Formulae in the Quaternionic Context; 1.6 Future Work and Ideas; References; 2 Quaternionic Hyperbolic Function Theory; 2.1 Introduction; 2.2 Preliminaries; 2.3 Hyperregular Functions; 2.4 Cauchy Type Integral Formulas; 2.5 Conclusion; References; 3 Slice Regularity and Harmonicity on Clifford Algebras
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3.1 Introduction and Preliminaries3.2 The Slice Derivatives and the Operator; 3.3 Spherical Operators; 3.4 The Laplacian of Slice Functions; 3.5 The Four-Dimensional Case: Zonal Harmonics and the Poisson Kernel; 3.6 The Quaternionic Case; References; 4 Some Notions of Subharmonicity over the Quaternions; 4.1 Introduction; 4.2 Prerequisites; 4.3 Quaternionic Notions of Subharmonicity; 4.4 Composition with Regular Functions; 4.5 Mean-Value Property and Consequences; 4.6 Approximation; 4.7 Green's Functions; 4.7.1 A Significant Example; Appendix; References
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7.1 Introduction7.2 Preliminaries; 7.3 Signumdistributions; 7.4 The Dirac Operator in Spherical Co-ordinates; 7.5 The Laplace Operator in Spherical Co-ordinates; 7.6 Radial and Angular Derivatives of Distributions; 7.7 Actions on Signumdistributions; 7.8 Composite Actions of Two Operators; 7.9 Division of (Signum)Distributions by r; 7.10 Two Families of Specific (Signum)Distributions; 7.11 Conclusion; References; 8 Applications of Parabolic Dirac Operators to the Instationary Viscous MHD Equations on Conformally Flat Manifolds; 8.1 Introduction; 8.2 Preliminaries
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8.2.1 The Quaternionic Operator Calculus8.3 The Incompressible In-Stationary MHD Equations Revisited in the Quaternionic Calculus; 8.4 The MHD Equations in the More General Context of Some Conformally Flat Spin 3-Manifolds; References; 9 Generalized Riesz Transforms, Quasi-Monogenic Functions and Frames; 9.1 Introduction; 9.2 Preliminaries; 9.2.1 Clifford Algebras; 9.2.2 Function Spaces; 9.3 Quasi-Monogenic Functions; 9.4 Lp Multiplier; 9.4.1 Riesz Transforms; 9.4.2 Linearized Riesz Transforms in R2; 9.4.3 Linearized Riesz Transforms in R3; 9.5 Frames; 9.5.1 Riesz Wavelet Frames
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Part II Applications to Elliptic Partial Differential Equations5 A Fatou Theorem and Poisson's Integral Representation Formula for Elliptic Systems in the Upper Half-Space; 5.1 Introduction; 5.2 Preliminary Matters; 5.3 Proofs of Main Results; References; 6 Hardy Spaces for the Three-Dimensional Vekua Equation; 6.1 Introduction; 6.2 Notation and Background for the Main Vekua Equation; 6.3 Hardy Spaces of Solutions of the Main Vekua Equation; 6.4 Boundary Vekua-Hardy Spaces; 6.4.1 The Vekua-Hilbert Transform; 6.5 Closing Remarks; References; 7 Radial and Angular Derivatives of Distributions
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| Abstract
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Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions. The unique starting point of Wolfgang Sprößigs work was the application of quaternionic analysis to elliptic differential equations and boundary value problems. Over the years, Clifford analysis has become a broad-based theory with a variety of applications both inside and outside of mathematics, such as higher-dimensional function theory, algebraic structures, generalized polynomials, applications of elliptic boundary value problems, wavelets, image processing, numerical and discrete analysis. The aim of this volume is to provide an essential overview of modern topics in Clifford analysis, presented by specialists in the field, and to honor the valued contributions to Clifford analysis made by Wolfgang Sprößig throughout his career.
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| Subject
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Clifford algebras.
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| Subject
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Clifford algebras.
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| Dewey Classification
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512/.57
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| LC Classification
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QA199
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| Added Entry
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Bernstein, Swanhild.
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