Noncommutative Functional Calculus
Theory and Applications of Slice Hyperholomorphic Functions
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ISBN-13:
9783034803243
Veröffentl:
2013
Einband:
Paperback
Erscheinungsdatum:
21.04.2013
Seiten:
228
Autor:
Fabrizio Colombo Politecnico Di Milano
Gewicht:
353 g
Format:
235x155x13 mm
Serie:
289, Progress in Mathematics
Sprache:
Englisch
Beschreibung:
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.
This book shows that the Riesz-Dunford functional calculus can be extended to n-tuples of not necessarily commuting operators. To do so, the authors develop a completely new spectral theory.
1 Introduction.- 2 Slice monogenic functions.- 3 Functional calculus forntuples of operators.- 4 Quaternionic Functional Calculus.- 5 Appendix: The Riesz-Dunford functional calculus.- Bibliography.- Index.
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