Preface.- An Asymptotic Equivalence Between Two Frame Perturbation Theorems - B. A. Bailey.- Growth Behavior and Zero Distribution of Maximally Convergent Rational Approximants - H.-P. Blatt, R. Grothmann, and R. K. Kovacheva.- Generalization of Polynomial Interpolation at Chebyshev Nodes - Debao Chen.- Green's Functions: Taking Another Look at Kernel Approximation, Radial Basis Functions, and Splines - Gregory E. Fasshauer.- Sparse Recovery Algorithms: Sufficient Conditions in terms of Restricted Isometry Constants - Simon Foucart.- Lagrange Interpolation and New Asymptotic Formulae for the Riemann Zeta Function - Michael I. Ganzburg.- Active GeometricWavelets - Itai Gershtansky, Shai Dekel, and Nira Dyn.- Interpolating Composite Systems - Philipp Grohs.- Wavelets and Framelets within the Framework of Nonhomogeneous Wavelet Systems - Bin Han.- Compactly Supported Shearlets - Gitta Kutyniok, Jakob Lemvig, and Wang-Q Lim.- Shearlets on Bounded Domains - Gitta Kutyniok and Wang-Q Lim.- On Christoffel Functions and Related Quantities for Compactly Supported Measures - D. S. Lubinsky.- Exact Solutions of Some Extremal Problems of Approximation Theory - A. L. Lukashov.- A Lagrange Interpolation Method by Trivariate Cubic C 1 Splines of Low Locality - G. N urnberger and G. Schneider.- Approximation of Besov Vectors by Paley-Wiener Vectors in Hilbert Spaces - Isaac Z. Pesenson and Meyer Z. Pesenson.- A Subclass of the Length Twelve ParameterizedWavelets - David W. Roach.- Geometric Properties of Inverse Polynomial Images - Klaus Schiefermayr.- On Symbolic Computation of Ideal Projectors and Inverse Systems - Boris Shekhtman.- The Dimension of the Space of Smooth Splines of Degree 8 on Tetrahedral Partitions - Xiquan Shi, Ben Kamau, Fengshan Liu, and Baocai Yin.- On Simultaneous Approximation in Function Spaces - Eyad Abu-Sirhan.- Chalmers-Metcalf Operator and Uniqueness of Minimal Projections in _ n Yen and _ n 1 Spaces - Leslaw Skrzypek.- The Polynomial Inverse Image Method - Vilmos Totik.- On Approximation of Periodic Analytic Functions by Linear Combinations of Complex Exponents - Vesselin Vatchev.- Matrix Extension with Symmetry and its Applications - Xiaosheng Zhuang.-
These proceedings were prepared in connection with the international conference Approximation Theory XIII, which was held March 7-10, 2010 in San Antonio, Texas. The conference was the thirteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 144 participants. Previous conferences in the series were held in Austin, Texas (1973, 1976, 1980, 1992), College Station, Texas (1983, 1986, 1989, 1995), Nashville, Tennessee (1998), St. Louis, Missouri (2001), Gatlinburg, Tennessee (2004), and San Antonio, Texas (2007).
Along with the many plenary speakers, the contributors to this proceedings provided inspiring talks and set a high standard of exposition in their descriptions of new directions for research. Many relevant topics in approximation theory are included in this book, such as abstract approximation, approximation with constraints, interpolation and smoothing, wavelets and frames, shearlets, orthogonal polynomials, univariate and multivariate splines, and complex approximation.