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Hypercomplex Analysis: New Perspectives and Applications

  • Fester Einband
  • 227 Seiten
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Hypercomplex analysis is the extension of complex analysis to higher dimensions where the concept of a holomorphic function is sub... Weiterlesen
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Beschreibung

Hypercomplex analysis is the extension of complex analysis to higher dimensions where the concept of a holomorphic function is substituted by the concept of a monogenic function. In recent decades this theory has come to the forefront of higher dimensional analysis. There are several approaches to this: quaternionic analysis which merely uses quaternions, Clifford analysis which relies on Clifford algebras, and generalizations of complex variables to higher dimensions such as split-complex variables. This book includes a selection of papers presented at the session on quaternionic and hypercomplex analysis at the ISAAC conference 2013 in Krakow, Poland. The topics covered represent new perspectives and current trends in hypercomplex analysis and applications to mathematical physics, image analysis and processing, and mechanics.



Covers developments in all directions of hypercomplex analysis

Presents new perspectives and current trends for researchers interested in or related to the topic

Includes contributions written by leading experts in the field

Includes applications (image analysis, mathematical physics and mechanics, etc.) for persons working in these areas



Inhalt

Symmetries and associated pairs in quaternionic analysis.- Generalized quaternionic Schur functions in the ball and half-space and Krein-Langer factorization.- The Fock space in the slice hyperholomorphic setting.- Multi Mq-monogenic function in different dimension.- The fractional monogenic signal.- Weighted Bergman spaces.- On Appell sets and Verma modules for sl(2).- Integral formulas for k-hypermonogenic functions in R3.- Spectral properties of compact normal quaternionic operators.- Three-dimensional quaternionic analogue of the Kolosov-Muskhelishvili formulae.- On the continuous coupling of finite elements with holomorphic basis functions.- On psi-hyperholomorphic functions and a decomposition of harmonics.- Fractional Clifford analysis.- Spectral properties of differential equations in Clifford algebras.- Differential equations in multicomplex spaces.

Produktinformationen

Titel: Hypercomplex Analysis: New Perspectives and Applications
Editor:
EAN: 9783319087702
ISBN: 978-3-319-08770-2
Format: Fester Einband
Herausgeber: Springer, Berlin
Genre: Mathematik
Anzahl Seiten: 227
Gewicht: 492g
Größe: H17mm x B246mm x T155mm
Jahr: 2014
Auflage: 2014

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