Motivated by applications, an underlying theme in analysis is that
of finding bases and understanding the transforms that implement
them. These may be based on Fourier techniques or involve wavelet
tools; they may be orthogonal or have redundancies (e.g., frames
from signal analysis).
Representations, Wavelets, and Frames contains chapters
pertaining to this theme from experts and expositors of renown in
mathematical analysis and representation theory. Topics are
selected with an emphasis on fundamental and timeless techniques
with a geometric and spectral-theoretic flavor. The material is
self-contained and presented in a pedagogical style that is
accessible to students from both pure and applied mathematics while
also of interest to engineers.
The book is organized into five sections that move from the
theoretical underpinnings of the subject, through geometric
connections to tilings, lattices and fractals, and concludes with
analyses of computational schemes used in communications
engineering. Within each section, individual chapters present new
research, provide relevant background material, and point to new
trends and open questions.
Contributors: C. Benson, M. Bownik, V. Furst, V. W. Guillemin,
B. Han, C. Heil, J.A. Hogan, P.E.T. Jorgensen, K. Kornelson, J.D.
Lakey, D.R. Larson, K.D. Merrill, J.A. Packer, G. Ratcliff, K.
Shuman, M.-S. Song, D.W. Stroock, K.F. Taylor, E. Weber, X.
Zhang.
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