Hypercomplex Analysis: New Perspectives and Applications

Hypercomplex Analysis: New Perspectives and Applications

Paperback(Softcover reprint of the original 1st ed. 2014)

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Overview

Hypercomplex Analysis: New Perspectives and Applications by Swanhild Bernstein

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.

Product Details

ISBN-13: 9783319353623
Publisher: Springer International Publishing
Publication date: 10/07/2016
Series: Trends in Mathematics
Edition description: Softcover reprint of the original 1st ed. 2014
Pages: 227
Product dimensions: 6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

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.

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