Frames and Operator Theory in Analysis and Signal Processing (eBook)

This volume contains articles based on talks presented at the Special Session Frames and Operator Theory in Analysis and Signal Processing, held in San Antonio, Texas, in January of 2006. Recently, the field of frames has undergone tremendous advancement. Most of the work in this field is focused on the design and construction of more versatile frames and frames tailored towards specific applications, e.g., finite dimensional uniform frames for cellular communication. In addition, frames are now becoming a hot topic in mathematical research as a part of many engineering applications, e.g., matching pursuits and greedy algorithms for image and signal processing. Topics covered in this book include: Application of several branches of analysis (e.g., PDEs; Fourier, wavelet, and harmonic analysis; transform techniques; data representations) to industrial and engineering problems, specifically image and signal processing. Theoretical and applied aspects of frames and wavelets. Pure aspects of operator theory emphasizing the connections to applied mathematics, frames, and signal processing. This volume will be equally attractive to pure mathematicians working on the foundations of frame and operator theory and their interconnections as it will to applied mathematicians investigating applications and to physicists and engineers employing these designs. It thus may appeal to a wide target group of researchers and may serve as a catalyst for cross-fertilization of several important areas of mathematics and the applied sciences.