Ebook: Recent Advances in Harmonic Analysis and Applications: In Honor of Konstantin Oskolkov

Recent Advances in Harmonic Analysis and Applications features selected contributions from the AMS conference which took place at Georgia Southern University, Statesboro in 2011 in honor of Professor Konstantin Oskolkov's 65th birthday. The contributions are based on two special sessions, namely "Harmonic Analysis and Applications" and "Sparse Data Representations and Applications." Topics covered range from Banach space geometry to classical harmonic analysis and partial differential equations. Survey and expository articles by leading experts in their corresponding fields are included, and the volume also features selected high quality papers exploring new results and trends in Muckenhoupt-Sawyer theory, orthogonal polynomials, trigonometric series, approximation theory, Bellman functions and applications in differential equations.

Graduate students and researchers in analysis will be particularly interested in the articles which emphasize remarkable connections between analysis and analytic number theory. The readers will learn about recent mathematical developments and directions for future work in the unexpected and surprising interaction between abstract problems in additive number theory and experimentally discovered optical phenomena in physics. This book will be useful for number theorists, harmonic analysts, algorithmists in multi-dimensional signal processing and experts in physics and partial differential equations.

Recent Advances in Harmonic Analysis and Applications is dedicated to the 65th birthday of Konstantin Oskolkov and features contributions from analysts around the world.

The volume contains expository articles by leading experts in their fields, as well as selected high quality research papers that explore new results and trends in classical and computational harmonic analysis, approximation theory, combinatorics, convex analysis, differential equations, functional analysis, Fourier analysis, graph theory, orthogonal polynomials, special functions, and trigonometric series.

Numerous articles in the volume emphasize remarkable connections between harmonic analysis and other seemingly unrelated areas of mathematics, such as the interaction between abstract problems in additive number theory, Fourier analysis, and experimentally discovered optical phenomena in physics. Survey and research articles provide an up-to-date account of various vital directions of modern analysis and will in particular be of interest to young researchers who are just starting their career. This book will also be useful to experts in analysis, discrete mathematics, physics, signal processing, and other areas of science.

Recent Advances in Harmonic Analysis and Applications is dedicated to the 65th birthday of Konstantin Oskolkov and features contributions from analysts around the world.

The volume contains expository articles by leading experts in their fields, as well as selected high quality research papers that explore new results and trends in classical and computational harmonic analysis, approximation theory, combinatorics, convex analysis, differential equations, functional analysis, Fourier analysis, graph theory, orthogonal polynomials, special functions, and trigonometric series.

Numerous articles in the volume emphasize remarkable connections between harmonic analysis and other seemingly unrelated areas of mathematics, such as the interaction between abstract problems in additive number theory, Fourier analysis, and experimentally discovered optical phenomena in physics. Survey and research articles provide an up-to-date account of various vital directions of modern analysis and will in particular be of interest to young researchers who are just starting their career. This book will also be useful to experts in analysis, discrete mathematics, physics, signal processing, and other areas of science.

Content:
Front Matter....Pages i-xi
Front Matter....Pages 1-1
On the Scientific Work of Konstantin Ilyich Oskolkov....Pages 3-21
K. I. Oskolkov....Pages 23-25
My First Meetings with Konstantin Oskolkov....Pages 27-29
Meetings with Kostya Oskolkov....Pages 31-33
Konstantin Ilyich Oskolkov, Friend and Colleague....Pages 35-37
The Activity of K. I. Oskolkov in Nonlinear Approximation of Functions....Pages 39-41
How Young We Were....Pages 43-46
Front Matter....Pages 47-47
A Survey of Multidimensional Generalizations of Cantor’s Uniqueness Theorem for Trigonometric Series....Pages 49-61
On Fourier Multipliers Over Tube Domains....Pages 63-77
Multiparameter Projection Theorems with Applications to Sums-Products and Finite Point Configurations in the Euclidean Setting....Pages 79-91
Riesz Potentials, Bessel Potentials, and Fractional Derivatives on Besov-Lipschitz Spaces for the Gaussian Measure....Pages 93-103
Maximal Operators Associated to Sets of Directions of Hausdorff and Minkowski Dimension Zero....Pages 105-130
Distance Graphs in Vector Spaces Over Finite Fields....Pages 131-138
Remarks on Extremals in Minimal Support Inequalities....Pages 139-160
On Fubini Type Property in Lorentz Spaces....Pages 161-169
Some Applications of Equimeasurable Rearrangements....Pages 171-179
Maximal Functions Measuring Smoothness....Pages 181-196
Estimates for the Exceptional Lebesgue Sets of Functions from Sobolev Classes....Pages 197-223
Front Matter....Pages 225-234
Quest for Negative Dependency Graphs....Pages 235-242
A Quantitative Open Mapping Theorem for Quasi-Pseudonormed Groups....Pages 47-47
The Buckley Dyadic Square Function....Pages 243-258
Harmonic Analysis and Uniqueness Questions in Convex Geometry....Pages 259-286
Moduli of Smoothness and Rate of a.e. Convergence for Some Convolution Operators....Pages 287-302
The Path to ?-Bounded variation....Pages 303-316
Stability and Robustness of Weak Orthogonal Matching Pursuits....Pages 317-326
....Pages 327-337