Hypercomplex Analysis: New Perspectives and Applications [[electronic resource] /] / edited by Swanhild Bernstein, Uwe Kähler, Irene Sabadini, Frank Sommen
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| Titolo: |
Hypercomplex Analysis: New Perspectives and Applications [[electronic resource] /] / edited by Swanhild Bernstein, Uwe Kähler, Irene Sabadini, Frank Sommen
|
| Pubblicazione: | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2014 |
| Edizione: | 1st ed. 2014. |
| Descrizione fisica: | 1 online resource (228 p.) |
| Disciplina: | 515.9 |
| Soggetto topico: | Functions of complex variables |
| Topological groups | |
| Lie groups | |
| Computer mathematics | |
| Functions of a Complex Variable | |
| Topological Groups, Lie Groups | |
| Several Complex Variables and Analytic Spaces | |
| Computational Science and Engineering | |
| Persona (resp. second.): | BernsteinSwanhild |
| KählerUwe | |
| SabadiniIrene | |
| SommenFrank | |
| Note generali: | Description based upon print version of record. |
| Nota di bibliografia: | Includes bibliographical references at the end of each chapters. |
| Nota di contenuto: | ""Contents""; ""Preface""; ""Symmetries and Associated Pairs in Quaternionic Analysis""; ""1. Motivation and basic facts of quaternionic analysis""; ""2. Necessary and sufficient conditions for associated pairs""; ""3. First-order symmetries of the generalized Cauchy�Riemann operator""; ""4. Endomorphisms over the quaternions""; ""Acknowledgment""; ""References""; ""Generalized Quaternionic Schur Functions in the Ball and Half-space and Krein�Langer Factorization""; ""1. Introduction""; ""1.1. Some history""; ""1.2. The slice hyperholomorphic case""; ""2. A survey of the classical case"" |
| ""3. Slice hyperholomorphic functions and Blaschke products""""4. Some results from quaternionic functional analysis""; ""5. Generalized Schur functions and their realizations""; ""6. The factorization theorem""; ""7. The case of the half-space""; ""References""; ""The Fock Space in the Slice Hyperholomorphic Setting""; ""1. Introduction""; ""2. A brief survey of infinite-dimensional analysis""; ""3. The Fock space in the slice regular case""; ""4. Quaternion full Fock space and symmetric Fock space""; ""5. The slice monogenic case""; ""References"" | |
| ""Multi Mq-monogenic Function in Different Dimension""""1. Introduction""; ""2. Separately holomorphic and monogenic functions""; ""3. Clifford-algebra-valued functions in several variables""; ""4. Associated algebra of Clifford type 1""; ""4.1. Decomposition of the q-Cauchy�Riemann system""; ""5. Example 1""; ""6. Associated algebra of Clifford type 2""; ""7. Example 2""; ""8. Definition of separately Mq-monogenic functions""; ""9. Conclusions""; ""Acknowledgment""; ""References""; ""The Fractional Monogenic Signal""; ""1. Introduction""; ""2. Preliminaries""; ""2.1. Quaternions"" | |
| ""2.1.1. Real quaternions.""""2.1.2. Complex quaternions.""; ""2.2. Rotations""; ""2.3. Quaternionic analysis""; ""2.3.1. Dirac operator.""; ""2.3.2. Integral formulae.""; ""2.3.3. Hardy spaces.""; ""3. The analytic signal""; ""3.1. Hilbert transform""; ""3.2. Fractional Hilbert operator and analytic fractional signal""; ""4. The fractional Riesz operator""; ""4.1. The isoclinic fractional Riesz transform""; ""4.2. Properties of the fractional Riesz operator""; ""5. Fractional monogenic signal""; ""5.1. Properties of the fractional monogenic signal""; ""6. Concluding remarks""; ""References"" | |
| ""Weighted Bergman Spaces""""1. Introduction""; ""2. The α-Bloch�Bergman space""; ""3. Properties of A and L(p,q,s)""; ""5. Strict inclusions of the spaces A(p,q,s)""; ""6. F(p,q,s) and A spaces""; ""7. Carleson measures""; ""Acknowledgment""; ""References""; ""On Appell Sets and Verma Modules for sl(2)""; ""1. Introduction""; ""2. Appell sets in Verma modules for sl(2)""; ""3. Hermite bases in Verma modules for sl(2)""; ""References""; ""Integral Formulas for k-hypermonogenic Functions in R3""; ""1. Introduction""; ""2. Preliminaries"" | |
| ""3. Integral formulas for k-hypermonogenic functions"" | |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | Hypercomplex analysis |
| ISBN: | 3-319-08771-1 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910299984603321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Trends in Mathematics, . 2297-0215