Graziano Gentili, Caterina Stoppato, Daniele C. Struppa

Regular Functions of a Quaternionic Variable (eBook, PDF)

• Format: PDF

Produktbeschreibung

>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. ¿

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 185
• Erscheinungstermin: 11. Januar 2013
• Englisch
• ISBN-13: 9783642338717
• Artikelnr.: 37737820

Inhaltsangabe

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.- 11. Function Theory over Non-symmetric Slice Domains.-12. Applications.- Bibliography.- Index.