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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