Approximation Theory X: Abstract and Classical Analysis

Charles K. Chui, Larry L. Schumaker, and Joachim Stöckler (eds.)

Vanderbilt University Press, Nashville, 2002

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . vii

Contributors . . . . . . . . . . . . . . . . . . . . . . . . viii

Rate of Convergence of Bounded Linear Operators George Anastassiou . . . . . . . . . . . . . . . . . . . . . 1

The Metric Average of 1D Compact Sets Robert Baier, Nira Dyn and Elza Farkhi . . . . . . . . . . . . 9

Uniform Strong Unicity of Order 2 for Generalized Haar Sets M. W. Bartelt and J. J. Swetits . . . . . . . . . . . . . . . . 23

Markov-type Inequalities for Polynomials and Splines Borislav Bojanov . . . . . . . . . . . . . . . . . . . . . . 31

Nonlinear Approximation by Refinable Functions and Piecewise Polynomials

Yu. Brudnyi . . . . . . . . . . . . . . . . . . . . . . . 91

On Spaces Admitting Minimal Projections Which are Orthogonal Bruce L. Chalmers and Boris Shekhtman . . . . . . . . . . 113

Hilbert Transforms and Orthonormal Expansions for Exponential Weights

S. B. Damelin . . . . . . . . . . . . . . . . . . . . . . 117

On the Separation of Logarithmic Points on the Sphere P. D. Dragnev . . . . . . . . . . . . . . . . . . . . . . 137

Best One–Sided L^{1}–Approximation by Blending Functions and Approximate Cubature

Dimiter Dryanov, Werner Haußmann and Petar Petrov …. 145

Polynomials with Littlewood-Type Coefficient Constraints Tamás Erdélyi . . . . . . . . . . . . . . . . . . . . . . 153

Parameterization of Manifold Triangulations Michael S. Floater, Kai Hormann, and Martin Reimers …. 197

Limit Theorems for Polynomial Approximations with Hermite and Freud Weights

Michael I. Ganzburg . . . . . . . . . . . . . . . . . . . 211 Complex Haar Spaces Generated by Shifts Applied to a Single Function

Walter Hengartner and Gerhard Opfer . . . . . . . . . . . 223

Optimal Location with Polyhedral Constraints R. Huotari, M. P. Prophet, and J. Ribando . . . . . . . . . . 239

Non-degenerate Rational Approximation Franklin Kemp . . . . . . . . . . . . . . . . . . . . . . 247

L_{p} Markov–Bernstein Inequalities on All Arcs of the Circle for Generalized Polynomials

C. K. Kobindarajah . . . . . . . . . . . . . . . . . . . 267

Positive Definite Kernel Interpolation on Manifolds: Convergence Rates

Jeremy Levesley and David L. Ragozin . . . . . . . . . . . 277

Asymptotic Expressions for Multivariate Positive Linear Operators

A.-J. López-Moreno, J. Martínez-Moreno and F. J. Muñoz-Delgado 287

Approximation by Penalized Least Squares José L. Martínez-Morales . . . . . . . . . . . . . . . . . 309

Conditions of Regularity for Bernstein–Rogosinski-type Means of Double Fourier Series

Yuri Nosenko . . . . . . . . . . . . . . . . . . . . . . 325

Some Remarks on Zero-Increasing Transformations Allan Pinkus . . . . . . . . . . . . . . . . . . . . . . . 333

The Aitken–Neville Scheme in Several Variables Thomas Sauer and Yuesheng Xu . . . . . . . . . . . . . . 353

Interpolation by Polynomials in Several Variables Boris Shekhtman . . . . . . . . . . . . . . . . . . . . . 367

Nonlinear Approximation with Regard to Bases V. N. Temlyakov . . . . . . . . . . . . . . . . . . . . . 373