This book is based on lectures given at the Global Analysis
Research Center (GARC) of Seoul National University in 1999and at
Peking University in 1999and 2000. Preliminary versions of the book
have been used for various topics courses in analysis for graduate
students at York University. We study in this book wavelet
transforms and localization operators in the context of
infinite-dimensional and square-integrable representations of
locally compact and Hausdorffgroups. The wavelet transforms studied
in this book, which include the ones that come from the
Weyl-Heisenberg group and the well-known affine group, are the
building blocks of localization operators. The theme that dominates
the book is the spectral theory of wavelet transforms and
localization operators in the form of Schatten-von Neumann norm
inequalities. Several chap ters are also devoted to the product
formulas for concrete localization operators such as Daubechies
operators and wavelet multipliers. This book is a natural sequel to
the book on pseudo-differential operators [103] and the book on
Weyl transforms [102] by the author. Indeed, localization operators
on the Weyl-Heisenberg group are Weyl transforms, which are in fact
pseudo-differential operators. Details on the perspective and the
organization of the book are laid out in the first chapter. This is
a book on mathematics and is written for anyone who has taken basic
graduate courses in measure theory and functional analysis. Some
knowledge of group theory and general topology at the undergraduate
level is also assumed.
General
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