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Cover: 9783319087702 | Hypercomplex Analysis: New Perspectives and Applications | Buch | vii
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Hypercomplex Analysis: New Perspectives and Applications
Buch von Swanhild Bernstein (u. a.)
Sprache: Englisch

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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.
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.
Zusammenfassung

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

Includes supplementary material: [...]

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2014
Fachbereich: Analysis
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Trends in Mathematics
Inhalt: vii
227 S.
ISBN-13: 9783319087702
ISBN-10: 3319087703
Sprache: Englisch
Herstellernummer: 86330088
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Bernstein, Swanhild
Kähler, Uwe
Sabadini, Irene
Sommen, Frank
Redaktion: Bernstein, Swanhild
Sommen, Frank
Sabadini, Irene
Kähler, Uwe
Herausgeber: Swanhild Bernstein/Uwe Kähler/Irene Sabadini et al
Hersteller: Springer International Publishing
Springer International Publishing AG
Trends in Mathematics
Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße: 241 x 160 x 19 mm
Von/Mit: Swanhild Bernstein (u. a.)
Erscheinungsdatum: 27.10.2014
Gewicht: 0,524 kg
Artikel-ID: 105193195
Zusammenfassung

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

Includes supplementary material: [...]

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2014
Fachbereich: Analysis
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Trends in Mathematics
Inhalt: vii
227 S.
ISBN-13: 9783319087702
ISBN-10: 3319087703
Sprache: Englisch
Herstellernummer: 86330088
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Bernstein, Swanhild
Kähler, Uwe
Sabadini, Irene
Sommen, Frank
Redaktion: Bernstein, Swanhild
Sommen, Frank
Sabadini, Irene
Kähler, Uwe
Herausgeber: Swanhild Bernstein/Uwe Kähler/Irene Sabadini et al
Hersteller: Springer International Publishing
Springer International Publishing AG
Trends in Mathematics
Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße: 241 x 160 x 19 mm
Von/Mit: Swanhild Bernstein (u. a.)
Erscheinungsdatum: 27.10.2014
Gewicht: 0,524 kg
Artikel-ID: 105193195
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