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Noncommutative Functional Calculus

Theory and Applications of Slice Hyperholomorphic Functions

Springer Basel,
Buch
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Kurzbeschreibung

This exposition of the new functional calculus methodology, as well as its analog for quaternionic linear operators is informed by the recently developed theory of hyperholomorphicity and is ideal for application to n-tuples of non-commuting linear operators.

Details
Schlagworte
Hauptbeschreibung

Titel: Noncommutative Functional Calculus
Autoren/Herausgeber: Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa
Aus der Reihe: Progress in Mathematics
Ausgabe: 2011

ISBN/EAN: 9783034801096

Seitenzahl: 222
Format: 23,5 x 15,5 cm
Produktform: Hardcover/Gebunden
Gewicht: 508 g
Sprache: Englisch

This book presents a functional calculus for n-tuples of not necessarily commuting linear operators. In particular, a functional calculus for quaternionic linear operators is developed. These calculi are based on a new theory of hyperholomorphicity for functions with values in a Clifford algebra: the so-called slice monogenic functions which are carefully described in the book. In the case of functions with values in the algebra of quaternions these functions are named slice regular functions. Except for the appendix and the introduction all results are new and appear for the first time organized in a monograph. The material has been carefully prepared to be as self-contained as possible. The intended audience consists of researchers, graduate and postgraduate students interested in operator theory, spectral theory,  hypercomplex analysis, and mathematical physics.

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