Noncommutative Functional Calculus: Theory and Applications of Slice Hyperholomorphic Functions
Noncommutative Functional Calculus: Theory and Applications of Slice Hyperholomorphic Functions By Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa (auth.)
2011 | 222 Pages | ISBN: 3034801092 | PDF | 3 MB
2011 | 222 Pages | ISBN: 3034801092 | PDF | 3 MB
<i>This book presents a functional calculus for <i>n</i>-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.</i><br> <p>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.</p>