Over the past decade, wavelets and frames have emerged as increasingly powerful tools of analysis on \(n\)-dimension Euclidean space. Both wavelets and frames were studied initially by using classical Fourier analysis. However, in recent years more abstract tools have been introduced, for example, from operator theory, abstract harmonic analysis, von Neumann algebras, etc.

The editors of this volume organized a Special Session on the functional and harmonic analysis of wavelets at the San Antonio (TX) Joint Mathematics Meetings. The goal of the session was to focus research attention on these newly-introduced tools and to share the organizers' view that this modern application holds the promise of providing some deeper understanding and fascinating new structures in pure functional analysis. This volume presents the fruitful results of the lively discussions that took place at the conference.

Readership

Graduate students and research mathematicians interested in analysis.

Table of Contents

• A. Aldroubi and P. Basser -- Reconstruction of vector and tensor fields from sampled discrete data
• L. W. Baggett and K. D. Merrill -- Abstract harmonic analysis and wavelets in \(\mathbb{R}^n\)
• R. Balan -- Density and redundancy of the noncoherent Weyl-Heisenberg superframes
• J. J. Benedetto and M. T. Leon -- The construction of multiple dyadic minimally supported frequency wavelets on \(\mathbb{R}^d\)
• L. Brandolini, G. Garrigós, Z. Rzeszotnik, and G. Weiss -- The behaviour at the origin of a class of band-limited wavelets
• O. Bratteli and P. E. T. Jorgensen -- Convergence of the cascade algorithm at irregular scaling functions
• P. G. Casazza, O. Christensen, and A. J. E. M. Janssen -- Classifying tight Weyl-Heisenberg frames
• P. G. Casazza, D. Han, and D. R. Larson -- Frames for Banach spaces
• J. Courter -- Construction of dilation-\(d\) wavelets
• M. Frank and D. R. Larson -- A module frame concept for Hilbert C*-modules
• J. Gasch and J. E. Gilbert -- Triangularization of Hankel operators and the bilinear Hilbert transform
• R. F. Gundy -- Two remarks concerning wavelets: Cohen's criterion for low-pass filters and Meyer's theorem on linear independence
• D. Han, D. R. Larson, M. Papadakis, and Th. Stavropoulos -- Multiresolution analyses of abstract Hilbert spaces and wandering subspaces
• G. Strang, V. Strela, and D.-X. Zhou -- Compactly supported refinable functions with infinite masks
• E. Weber -- Applications of the wavelet multiplicity function