Regular functions of a quaternionic variable
The theory of slice regular functions over quaternions is the central subject of the present volume. This recent theory has expanded rapidly, producing a variety of new results that have caught the attention of the international research community. At the same time, the theory has already developed...
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| Auteurs principaux: | , , |
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| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Édition: | 1st ed. 2013. |
| Collection: | Springer Monographs in Mathematics
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| Sujets: | |
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
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Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Regular Functions of a Quaternionic Variable, Texte imprimé, 9783642338724 • Regular Functions of a Quaternionic Variable, Texte imprimé, 9783642440540 • Regular Functions of a Quaternionic Variable, Texte imprimé, 9783642338700 |
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| 100 | 1 | |a Gentili, Graziano, |d 19..-...., |c mathématicien. | |
| 245 | 1 | 0 | |a Regular functions of a quaternionic variable |c by Graziano Gentili, Caterina Stoppato, Daniele C. Struppa. |
| 250 | |a 1st ed. 2013. | ||
| 260 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Springer Monographs in Mathematics |x 2196-9922 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliographie. Notes bibliogr. Index | ||
| 505 | 1 | |a Introduction 1.Definitions and Basic Results 2.Regular Power Series 3.Zeros 4.Infinite Products 5.Singularities 6.Integral Representations 7.Maximum Modulus Theorem and Applications 8.Spherical Series and Differential 9.Fractional Transformations and the Unit Ball 10.Generalizations and Applications Bibliography Index. | |
| 505 | 0 | |a Introduction -- 1.Definitions and Basic Results -- 2.Regular Power Series -- 3.Zeros -- 4.Infinite Products -- 5.Singularities -- 6.Integral Representations -- 7.Maximum Modulus Theorem and Applications -- 8.Spherical Series and Differential -- 9.Fractional Transformations and the Unit Ball -- 10.Generalizations and Applications -- Bibliography -- aIndex | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a The theory of slice regular functions over quaternions is the central subject of the present volume. This recent theory has expanded rapidly, producing a variety of new results that have caught the attention of the international research community. At the same time, the theory has already developed sturdy foundations. The richness of the theory of the holomorphic functions of one complex variable and its wide variety of applications are a strong motivation for the study of its analogs in higher dimensions. In this respect, the four-dimensional case is particularly interesting due to its relevance in physics and its algebraic properties, as the quaternion forms the only associative real division algebra with a finite dimension n>2. Among other interesting function theories introduced in the quaternionic setting, that of (slice) regular functions shows particularly appealing features. For instance, this class of functions naturally includes polynomials and power series. The zero set of a slice regular function has an interesting structure, strictly linked to a multiplicative operation, and it allows the study of singularities. Integral representation formulas enrich the theory and they are a fundamental tool for one of the applications, the construction of a noncommutative functional calculus. The volume presents a state-of-the-art survey of the theory and a brief overview of its generalizations and applications. It is intended for graduate students and researchers in complex or hypercomplex analysis and geometry, function theory, and functional analysis in general. | ||
| 650 | |a Fonctions d'une variable complexe | ||
| 650 | |a Polynômes | ||
| 650 | |a Fonctions quaternioniennes | ||
| 700 | 1 | |a Stoppato, Caterina, |d 19..-...., |c mathématicienne. |4 aut | |
| 700 | 1 | |a Struppa, Daniele Carlo, |d 1955- |4 aut | |
| 776 | 0 | |t Regular Functions of a Quaternionic Variable |b Texte imprimé |z 9783642338724 | |
| 776 | 0 | |t Regular Functions of a Quaternionic Variable |b Texte imprimé |z 9783642440540 | |
| 776 | 0 | |t Regular Functions of a Quaternionic Variable |b Texte imprimé |z 9783642338700 | |
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