Details
Noncommutative Functional Calculus
Theory and Applications of Slice Hyperholomorphic FunctionsProgress in Mathematics, Band 289
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53,49 € |
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| Verlag: | Birkhäuser |
| Format: | |
| Veröffentl.: | 18.03.2011 |
| ISBN/EAN: | 9783034801102 |
| Sprache: | englisch |
| Anzahl Seiten: | 222 |
Dieses eBook enthält ein Wasserzeichen.
Beschreibungen
<p><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></p><p><br> </p><p><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></p>
<p>1 Introduction.- 2 Slice monogenic functions.- 3 Functional calculus for <i>n</i>-tuples of operators.- 4 Quaternionic Functional Calculus.- 5 Appendix: The Riesz-Dunford functional calculus.- Bibliography.- Index.</p>
<p><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></p><p><br> </p><p><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></p><p>
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. 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. Includes supplementary material: sn.pub/extras
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