Approximation Theory XVI Nashville, TN, USA, May 19-22, 2019

These proceedings are based on the international conference Approximation Theory XVI held on May 19–22, 2019 in Nashville, Tennessee. The conference was the sixteenth in a series of meetings in Approximation Theory held at various locations in the United States.  Over 130 mathematicians from 20 countries attended.  The book contains two longer survey papers on nonstationary subdivision and Prony’s method, along with 11 research papers on a variety of topics in approximation theory, including Balian-Low theorems, butterfly spline interpolation, cubature rules, Hankel and Toeplitz matrices, phase retrieval, positive definite kernels, quasi-interpolation operators, stochastic collocation, the gradient conjecture, time-variant systems, and trivariate finite elements. The book should be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.

Time-variant System Approximation via later-time Samples.- C1-quartic Butterfly-spline Interpolation on Type-1 Triangulations.- Approximation with Conditionally Positive Definite Kernels on Deficient Sets.- Non-stationary Subdivision Schemes: State of the Art and Perspectives.- Cubature Rules Based on Bivariate Spline Quasi-interpolation for Weakly Singular Integrals.- On DC based Methods for Phase Retrieval.- Modifications of Pronys Method for the Recovery and Sparse Approximation of Generalized Exponential Sums.- On Eigenvalue Distribution of Varying Hankel and Toeplitz Matrices with Entries of Power Growth or Decay.- On the Gradient Conjecture for Quadratic Polynomials.- Balian-Low Theorems in Several Variables.- Quasi-Interpolant Operators and the Solution of Fractional Differential Problems.- Stochastic Collocation with Hierarchical Extended B-splines on Sparse Grids.- Trivariate Interpolated Galerkin Finite Elements for the Poisson Equation.- Index.

Marian Neamtu is Professor and Chair of the Department of Mathematics at Vanderbilt University. His current research interests are in approximation theory, splines, geometric design, and numerical analysis.

Larry L. Schumaker is Stevenson Professor of Mathematics at Vanderbilt University.  He is a fellow of the AMS, a SIAM fellow, and a member of the Norwegian Academy of Sciences.  He is the author of three books on splines, and is a co-editor of over 40 proceedings volumes.  He continues to do research on splines and their applications.