The Norbert Wiener Center for Harmonic Analysis and Applications provides a state-of-the-art research venue for the broad emerging area of mathematical engineering in the context of harmonic analysis.
This two-volume set consists of contributions from speakers at the February Fourier Talks (FFT) from 2006-2011. The FFT are organized by the Norbert Wiener Center in the Department of Mathematics at the University of Maryland, College Park. These volumes span a large spectrum of harmonic analysis and its applications. They are divided into the following parts:
· Sampling Theory
· Remote Sensing
· Mathematics of Data Processing
· Applications of Data Processing
· Measure Theory
· Operator Theory
Each part provides state-of-the-art results, with contributions from an impressive array of mathematicians, engineers, and scientists in academia, industry, and government.
Excursions in Harmonic Analysis: The February Fourier Talks at the Norbert Wiener Center is an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.
Table of Contents
Part V Measure Theory.- Absolute Continuity and Singularity of Measures Without Measure Theory.- Visible and Invisible Cantor Sets.- Convolution Inequalities for Positive Borel Measures on Rsubd and Beurling Density.- Positive Operator-Valued Measures: A General Setting for Frames.- Part VI Filtering.- Extending Wavelet Filters, Infinite Dimensions, the Non-Rational Case, and Indefinite-Inner Product Spaces.- On the Group-Theoretic Structure of Lifted Filter Banks.- Parametric Optimization of Biorthogonal Wavelets and Filterbanks via Pseudoframes for Subspaces.- On the Convergence of Iterative Filtering Empirical Mode Decomposition.- Wavelet Transforms by Nearest Neighbor Lifting.- Part VII Operator Theory.- On the Heat Kernel of a Left Invariant Elliptic Operator.- Mixed-Norm Estimates for the k-Plane Transform.- Representation of Linear Operators by Gabor Multipliers.- Extensions of Berezin-Lieb Inequalities.- Bilinear Calderon-Zygmund Operators.- Weighted Inequalities and Dyadic Harmonic Analysis.- Part VIII Biomathematics.- Enhancement and Recovery in Atomic Force Micosopy Images.- Numerical Harmonic Analysis and Diffusions on the 3D-Motion Group.- Quantification of Retinal Chromophores Through Autofluorescence Imaging to Identify Precursors of Age-Related Macular .- Simple Harmonic Oscillator Based Reconstruction and Estimation for One-Dimensional q-Space Magnetic Resonance (1D-SHORE).- Fourier Blues: Structural Coloration of Biological Tissues.- A Harmonic Analysis View On Neuroscience Imaging.