## Approximation Theory XIII: San Antonio 2010Marian Neamtu, Larry L. Schumaker 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. |

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### Contents

2 | |

Growth Behavior and Zero Distribution of Maximally Convergent Rational Approximants | 9 |

Generalization of Polynomial Interpolation at Chebyshev Nodes | 17 |

Taking Another Look at Kernel Approximation Radial Basis Functions and Splines | 37 |

Sufficient Conditions in Terms of Restricted Isometry Constants | 64 |

Lagrange Interpolation and New Asymptotic Formulae for the Riemann Zeta Function | 79 |

Active Geometric Wavelets | 94 |

Interpolating Composite Systems | 111 |

A Lagrange Interpolation Method by Trivariate Cubic C1 Splines of Low Locality | 231 |

Approximation of Besov Vectors by PaleyWiener Vectors in Hilbert Spaces | 249 |

A Subclass of the Length 12 Parameterized Wavelets | 263 |

Geometric Properties of Inverse Polynomial Images | 276 |

On Symbolic Computation of Ideal Projectors and Inverse Systems | 289 |

The Dimension of the Space of Smooth Splines of Degree 8 on Tetrahedral Partitions | 296 |

On Simultaneous Approximation in Function Spaces | 321 |

ChalmersMetcalf Operator and Uniqueness of Minimal Projections in ln and ln1 Spaces
| 331 |

Wavelets and Framelets Within the Framework of Nonhomogeneous Wavelet Systems | 121 |

Compactly Supported Shearlets | 162 |

Shearlets on Bounded Domains | 187 |

On Christoffel Functions and Related Quantities for Compactly Supported Measures | 207 |

Exact Solutions of Some Extremal Problemsof Approximation Theory | 221 |

The Polynomial Inverse Image Method | 345 |

On Approximation of Periodic Analytic Functions by Linear Combinations of Complex Exponents | 366 |

Matrix Extension with Symmetryand Its Applications | 375 |