## Approximation theory: proceedings of the International Dortmund Meeting, IDoMAT 95 held in Witten, Germany, March 13-17, 1995This volume contains the contributions of the International Dortmund Meeting on Approximation Theory (IDoMAT 95) at Haus Bommerholz the conference center of Dortmund University during the week of March 13-17, 1995. At this international conference researchers and specialists from China, England, France, Hungary, Israel, Italy, Romania, U.S.A. and Germany described new developments in the fields of approximation theory. The authors discuss a variety of important ideas, questions and applicable methods in applied sciences and in several fields of approximation theory which lead to new challenges to the approximation by means of linear operators and shape preserving approximation, methods for the study of differential (diffusion) equations, approximation results of solutions of specific hyperbolic differential equations, polynomial and spline interpolation, density problems in multivariate approximation, orthogonal polynomials and wavelets. This volume collects the complete papers of the invited lectures together with a selection of papers relating to the research talks presented at IDoMAT 95. |

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### Contents

Approximation Theory Methods for the Study of Diffusion Equations | 9 |

The Approximation Theoretical Behaviour of Solutions of Specific Hyperbolic Differ | 27 |

Boundedness of Lagrange and Hermite Operators | 53 |

Copyright | |

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Akademie Verlag Altomare Approx Approximation Theory arbitrary assume Banach space Bernstein polynomials Chebyshev polynomials coefficients consider constant continuous functions Corollary cosine operator function D. H. Mache Mathematical defined denote density derivatives DeVore differential equation differential operator Dortmund Edited by M. W. equibounded estimates exists Felten finite fixed Fourier fur Mathematik g-normal given harmonic Hence holds true IDoMAT 95 inequality integral interval ISBN Jacobi polynomials K-functional Lehrstuhl Lemma Leviatan limsup linear operators linear positive operators lower bound Mache Mathematical Research Math modulus of continuity Moreover nondecreasing obtain operator norm orthogonal polynomials perturbations pointwise polynomial approximation polynomials of degree problem Proc proof of Theorem properties proved recurrence respectively satisfying self-reciprocal polynomials semigroup sequence sgn(x solution spline interpolation subspace Theorem 2.1 Totik uniform convergence Universitat Dortmund Vallee Poussin VERTESI wavelets Weighted polynomial zeros