Induced Representations of Locally Compact Groups

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Algebra
Cover of the book Induced Representations of Locally Compact Groups by Eberhard Kaniuth, Keith F. Taylor, Cambridge University Press
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Author: Eberhard Kaniuth, Keith F. Taylor ISBN: 9781139853552
Publisher: Cambridge University Press Publication: November 22, 2012
Imprint: Cambridge University Press Language: English
Author: Eberhard Kaniuth, Keith F. Taylor
ISBN: 9781139853552
Publisher: Cambridge University Press
Publication: November 22, 2012
Imprint: Cambridge University Press
Language: English

The dual space of a locally compact group G consists of the equivalence classes of irreducible unitary representations of G. This book provides a comprehensive guide to the theory of induced representations and explains its use in describing the dual spaces for important classes of groups. It introduces various induction constructions and proves the core theorems on induced representations, including the fundamental imprimitivity theorem of Mackey and Blattner. An extensive introduction to Mackey analysis is applied to compute dual spaces for a wide variety of examples. Fell's contributions to understanding the natural topology on the dual are also presented. In the final two chapters, the theory is applied in a variety of settings including topological Frobenius properties and continuous wavelet transforms. This book will be useful to graduate students seeking to enter the area as well as experts who need the theory of unitary group representations in their research.

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The dual space of a locally compact group G consists of the equivalence classes of irreducible unitary representations of G. This book provides a comprehensive guide to the theory of induced representations and explains its use in describing the dual spaces for important classes of groups. It introduces various induction constructions and proves the core theorems on induced representations, including the fundamental imprimitivity theorem of Mackey and Blattner. An extensive introduction to Mackey analysis is applied to compute dual spaces for a wide variety of examples. Fell's contributions to understanding the natural topology on the dual are also presented. In the final two chapters, the theory is applied in a variety of settings including topological Frobenius properties and continuous wavelet transforms. This book will be useful to graduate students seeking to enter the area as well as experts who need the theory of unitary group representations in their research.

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