## Frontiers in Interpolation and ApproximationDedicated to the well-respected research mathematician Ambikeshwar Sharma, Frontiers in Interpolation and Approximation explores approximation theory, interpolation theory, and classical analysis. Written by authoritative international mathematicians, this book presents many important results in classical analysis, wavelets, and interpolation theory. Some topics covered are Markov inequalities for multivariate polynomials, analogues of Chebyshev and Bernstein inequalities for multivariate polynomials, various measures of the smoothness of functions, and the equivalence of Hausdorff continuity and pointwise Hausdorff-Lipschitz continuity of a restricted center multifunction. The book also provides basic facts about interpolation, discussing classes of entire functions such as algebraic polynomials, trigonometric polynomials, and nonperiodic transcendental entire functions. Containing both original research and comprehensive surveys, this book provides researchers and graduate students with important results of interpolation and approximation. |

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### Contents

MarkovType Inequalities for Homogeneous Polynomials on Nonsymmetric StarLike Domains | 1 |

Local Inequalities for Multivariate Polynomials and Plurisubharmonic Functions | 17 |

The Norm of an Interpolation Operator on HD | 33 |

The Dutch Connection | 45 |

Freeness of Spline Modules from a Divided to a Subdivided Domain | 59 |

Measures of Smoothness on the Sphere | 75 |

Quadrature Formulae of Maximal Trigonometric Degree of Precision | 93 |

Inequalities for Exponential Sums via Interpolation and TuránType Reverse Markov Inequalities | 119 |

Lagrange Interpolation at Lacunary Roots of Unity | 249 |

A Fast Algorithm for Spherical Basis Approximation | 259 |

Direct and Converse Polynomial Approximation Theorems on the Real Line with Weights Having Zeros | 287 |

Fourier Sums and Lagrange Interpolation on 0+ and + | 307 |

On Bounded Interpolatory and QuasiInterpolatory Polynomial Operators | 345 |

Hausdorff Strong Uniqueness in Simultaneous Approximation | 365 |

Zeros of Polynomials Given as an Orthogonal Expansion | 381 |

Uniqueness of Tchebycheff Spaces and Their Ideal Relatives | 407 |

### Other editions - View all

Frontiers in Interpolation and Approximation N. K. Govil,H. N. Mhaskar,Ram N. Mohapatra,Zuhair Nashed,J. Szabados No preview available - 2006 |

### Common terms and phrases

Anal Approx Approximation Theory basis functions Birkhoff interpolation bounded C(Sd coefficients complex constant convergence d-complex defined degree of precision denote Department of Mathematics Email address entire function equations equiconvergence estimate exists exponential type finite Fourier function f given H. N. Mhaskar Hausdorff Hence Hermite interpolation hyperinterpolation I. J. Schoenberg ideal complement implies inequality integer interpolation problem K-functionals lacunary Lagrange interpolation Lagrange polynomial Lemma linear M. G. de Bruin Math matrix maximal trigonometric degree metric multifunction multiplicities nodes norm numerical integration rule obtain operator orthogonal polynomials Pn(Sd points polynomial interpolation polynomial of degree proof of Theorem proved quadrature formula real numbers roots of unity satisfying sequence smoothness solution sphere spherical splines subset subspace Szabados Tchebycheff spaces Theorem 2.1 tion trigono trigonometric interpolation trigonometric polynomial Turán uniformly unique zeros

### Popular passages

Page iii - ... Lecture Notes EXECUTIVE EDITORS Earl J. Taft Rutgers University New Brunswick, New Jersey Zuhair Nashed University of Delaware Newark, Delaware CHAIRMEN OF THE EDITORIAL BOARD S.

Page iv - Hansen and GW Walster, Global Optimization Using Interval Analysis: Second Edition, Revised and Expanded (2004) 265. MM Rao, Measure Theory and Integration: Second Edition, Revised and Expanded (2004) 266.

Page iii - Donald Passman University of Wisconsin, Madison Fred S. Roberts Rutgers University David L. Russell Virginia Polytechnic Institute and State University Walter Schempp Universitat Siegen Mark Teply University of Wisconsin, Milwaukee MONOGRAPHS AND TEXTBOOKS IN PURE AND APPLIED MATHEMATICS 1.

Page xvii - Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada, T2N 1N4 JH van Lint, Afdeling Wiskunde, TU Eindhoven, Postbus5I3, 5600 MB Eindhoven, The Netherlands R.