Noncommutative Functional Calculus

Theory and Applications of Slice Hyperholomorphic Functions
2011
ISBN: 978-3-0348-0109-6
Verlag: Springer

Buch, Englisch, Band 289, 222 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 512 g

Reihe: Progress in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Politecnico Di Milano, Fabrizio Colombo

Politecnico di Milano, Prof. Fabrizio Colombo

Struppa, Daniele C.

Sabadini, Irene

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

1 Introduction.- 2 Slice monogenic functions.- 3 Functional calculus for n-tuples of operators.- 4 Quaternionic Functional Calculus.- 5 Appendix: The Riesz-Dunford functional calculus.- Bibliography.- Index.