Noncommutative Functional Calculus - Theory and Applications of Slice Hyperholomorphic Functions

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.

List of contents

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.

Summary

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.

Product details

• Authors: Fabrizio Colombo, Fabrizio Colombo Politecnico di Milano, Prof Fabrizio Colomb Politecnico di Milano, Prof Fabrizio Colombo Politecnico di Milano, Prof. Fabrizio Colombo Politecnico di Milano, Sabad, Irene Sabadini, Daniele C. Struppa
• Publisher: Springer, Basel
• Languages: English
• Product format: Paperback / Softback
• Released: 11.04.2013
• EAN: 9783034803243
• ISBN: 978-3-0-3480324-3
• No. of pages: 222
• Dimensions: 156 mm x 238 mm x 14 mm
• Weight: 353 g
• Illustrations: VI, 222 p.
• Series: Progress in Mathematics; Progress in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; B, Mathematics and Statistics, Functional Analysis, Complex analysis, complex variables, Functional analysis & transforms, Operator Theory, Functions of a Complex Variable, Functions of complex variables