Operator Methods in Wavelets, Tilings, and Frames
About this Title
Veronika Furst, Fort Lewis College, Durango, CO, Keri A. Kornelson, University of Oklahoma, Norman, OK and Eric S. Weber, Iowa State University, Ames, IA, Editors
Publication: Contemporary Mathematics
Publication Year 2014: Volume 626
ISBNs: 978-1-4704-1040-7 (print); 978-1-4704-1957-8 (online)
This volume contains the proceedings of the AMS Special Session on Harmonic Analysis of Frames, Wavelets, and Tilings, held April 13–14, 2013, in Boulder, Colorado.
Frames were first introduced by Duffin and Schaeffer in 1952 in the context of nonharmonic Fourier series but have enjoyed widespread interest in recent years, particularly as a unifying concept. Indeed, mathematicians with backgrounds as diverse as classical and modern harmonic analysis, Banach space theory, operator algebras, and complex analysis have recently worked in frame theory. Frame theory appears in the context of wavelets, spectra and tilings, sampling theory, and more.
The papers in this volume touch on a wide variety of topics, including: convex geometry, direct integral decompositions, Beurling density, operator-valued measures, and splines. These varied topics arise naturally in the study of frames in finite and infinite dimensions. In nearly all of the papers, techniques from operator theory serve as crucial tools to solving problems in frame theory.
This volume will be of interest not only to researchers in frame theory but also to those in approximation theory, representation theory, functional analysis, and harmonic analysis.
Graduate students and research mathematicians interested in linear algebra, functional analysis, and operator theory.
Table of Contents
- Peter G. Casazza and Lindsey M. Woodland – Phase retrieval by vectors and projections
- Gitta Kutyniok, Kasso A. Okoudjou and Friedrich Philipp – Scalable frames and convex geometry
- Deguang Han, David R. Larson, Bei Liu and Rui Liu – Dilations of frames, operator-valued measures and bounded linear maps
- Mahya Ghandehari and Keith F. Taylor – Images of the continuous wavelet transform
- Bradley Currey, Azita Mayeli and Vignon Oussa – Decompositions of generalized wavelet representations
- Peter Massopust – Exponential splines of complex order
- Dorin Ervin Dutkay and John Haussermann – Local translations associated to spectral sets
- Palle E. T. Jorgensen, Keri A. Kornelson and Karen L. Shuman – Additive spectra of the $\frac 14$ Cantor measure
- Sa’ud al-Sa’di and Eric Weber – Necessary density conditions for sampling and interpolation in de Branges spaces
- Roza Aceska and Sui Tang – Dynamical sampling in hybrid shift invariant spaces
- Jacqueline Davis – Dynamical sampling in infinite dimensions with and without a forcing term