Hypercomplex analysis : new perspectives and applications
著者
書誌事項
Hypercomplex analysis : new perspectives and applications
（Trends in mathematics）
Birkhäuser : Springer, c2014
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注記
Other editors: Uwe Kähler, Irene Sabadini, Frank Sommen
"At the 9th International ISAAC Congress ... held at the Pedagogical University of Krakow, Krakow, Poland from August 5 to August 9, 2013 ... This volume contains a careful selection of 15 of these papers ..."--Preface
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
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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