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Topics in Clifford Analysis: Special Volume in Honor of Wolfgang Sprößig
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Catalogue Information
Field name
Details
Dewey Class
515.9
Title
Topics in Clifford Analysis ([EBook]) : Special Volume in Honor of Wolfgang Sprößig / edited by Swanhild Bernstein.
Added Personal Name
Bernstein, Swanhild
Other name(s)
SpringerLink (Online service)
Publication
Cham : Birkhäuser , 2019.
Physical Details
XXI, 503 pages, 22 illus., 10 illus. in color. : online resource.
Series
Trends in mathematics
ISBN
9783030238544
Summary Note
Quaternionic and Clifford analysis are an extension of complex analysis into higher dimensions. The unique starting point of Wolfgang Sprößig’s 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.:
Contents note
Part I - Clifford analysis theories -- Cauchy’s formula in Clifford analysis: An Overview -- Quaternionic Hyperbolic Function Theory -- Slice Regular and Harmonicity in Clifford Analysis -- Some notions of Subharmonicity over the Quaternions -- Part II - Applications to Elliptic Partial Differential Equations -- A Fatou Theorem and Poisson’s Integral Representation Formula for Elliptic Systems in the Upper-Half Space -- Hardy Spaces for Three-Dimensional Vekua Equation -- Radial and Angular Derivatives of Distributions -- Applications of Parabolic Dirac Operators to the Instationary Viscous MHD Equations on Conformally Flat Manifolds -- Generalized Riesz Transforms, Quasi-Monogenic Functions and Frames -- Part III - Monogenic Polynomials and Numerical Methods -- Quaternionic Operator Calculus for Boundary Value Problems of Micropolar Elasticity -- Constructive Orthonormalization of Monogenic Polynomials on a Finite Cylinder -- Comments on an Orthogonal Family of Monogenic Functions on Spheroidal Domains -- Newton’s Approach to General Algebra Equations over Clifford Algebras -- Part IV - Differential Geometry -- Connections in Euclidean and Non-Commutative Geometry -- Conformal Parametrisation of Loxodroms by Tripels of Circles -- Automorphic Forms and Dirac Operators on Conformally Flat manifolds -- Higher order Fermionic and Bosonic Operators -- Clifford Möbius Geometry -- Separation of Variables in the Semistable Range -- Variety of Idempotents in Nonassociative Algebras -- Part V - Discrete Clifford Analysis -- Relativistic Wave Equations on the Lattice: An Operational Perspective -- Cauchy-Pompeiu Formula for Discrete Monogenic Functions -- A Useful Transformation for Solving the Discrete Beltrami Equation and Reducing a Difference Equation of Second Order to a System of Equations of First Order.
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Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site
https://doi.org/10.1007/978-3-030-23854-4
Links to Related Works
Subject References:
Algebraic Geometry
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Clifford algebras
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Difference and Functional Equations
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Difference equations
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Field Theory and Polynomials
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Field theory (Physics)
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Functional equations
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Functions of complex variables
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Potential theory (Mathematics)
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Authors:
Bernstein, Swanhild
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editor
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Corporate Authors:
SpringerLink (Online service)
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Series:
Trends in mathematics
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Classification:
515.9
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515.9 (DDC 23)
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