Noncommutative functional calculus: theory and applications of slice hyperholomorphic functions

The book contains recent results concerning a functional calulus for n-tuplesof not necessarily commuting linear operators and for quaternionic linear operators. 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 and, in particular, for functions with values in the algebra of quaternions the so-called slice regular functions. All the results in the book are new (except for an Appendix on the Riesz-Dunford functional calculus and for a short introduction to Clifford algebras)and appear for the first time organized in a monograph. All the material presented is self contained. The intended audience consists of researcher in in operator theory, spectral theory, hypercomplex analysis, and mathematical physics as well as graduate and postgraduate students. This book shows that the Riesz-Dunford functional calculus can be extendedto n-tuples of not necessarily commuting operators. To do so, the authors develop a completely new spectral theory. The fundamental technical tools is the newly developed theory of slice hyperholomorphic functions (which includes functions of a paravector variable with values in a Clifford algebra and quaternionic valued functions of a quaternionic variable). The monograph is based on results by the authors and thus it is completely original, except for a few pages of basic material and an Appendix. INDICE: 1 Introduction. 2 Slice monogenic functions. 3 Functional calculusfor n -tuples of operators. 4 Quaternionic Functional Calculus. 5 Appendix: The Riesz-Dunford functional calculus. Bibliography. Index.

• ISBN: 978-3-0348-0109-6
• Editorial: Springer Basel
• Encuadernacion: Cartoné
• Páginas: 270
• Fecha Publicación: 30/04/2011
• Nº Volúmenes: 1
• Idioma: Inglés