Recent Advances in Approximation and Potential Theory

Over the course of his distinguished career, Edward Saff has made a number of groundbreaking contributions in the fields of approximation theory, potential theory, and complex analysis. The chapters in this volume compiled on the occasion of his 80th birthday are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.

Highlights Edward Saff's many significant mathematical contributions Explores the latest developments in approximation theory, potential theory, and related topics Features chapters written by distinguished mathematicians

Inhalt

Ed Saff at 80: Career and Distinguished Scientific Contributions.- Exponential bases on modified domains.- Positive definite singular kernels on two-point homogeneous spaces.- H¨ormander and Bernhardsson's extremal function I.- Absolute Minima of Potentials of a Certain Class of Spherical Designs.- Logarithmic and Riesz Energy on the Sphere: Better Bounds via elementary Methods.- Energy of codes with forbidden distances in 48 dimensions.- Frequency-dependent stability for Gabor frames.- A nonnegative even kernel arising from extremal sine polynomials.- The number of real zeros of polynomials with constrained coefficients.- Approximate orthogonality, Bourgain's pinned distance theorem, and exponential frames.- Application of Sparse Grids to Approximation and Optimization.- Shape preserving approximation of periodic functionsA survey.- Spaces of trigonometric series and the Wiener algebra.- Variational Conditions on Extremal Orthonormal Polynomials for Restricted Measures.- Behavior of bounded solutions, 𝑢(𝑥, 𝑡), to the heat equation in R𝑛 × (0, )as 𝑡 .- Weighted equilibrium and the flow of derivatives of polynomials.- A linear programming bound in a sign-alternating case.- Approximation by Fourier sums on the classes of generalized Poisson integrals.- On Linear Spaces with Ideal Complements.- On Analytic Functions with Taylor Coefficients Taken from a Finite Set.