Title | Advanced Problems in Constructive Approximation [electronic resource] : 3rd International Dortmund Meeting on Approximation Theory (IDoMAT) 2001 / edited by Martin D. Buhmann, Detlef H. Mache |
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Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2003 |

Connect to | http://dx.doi.org/10.1007/978-3-0348-7600-1 |

Descript | XIV, 274 p. online resource |

SUMMARY

The current form of modern approximation theory is shaped by many new deยญ velopments which are the subject of this series of conferences. The International Meetings on Approximation Theory attempt to keep track in particular of funยญ damental advances in the theory of function approximation, for example by (orยญ thogonal) polynomials, (weighted) interpolation, multivariate quasi-interpolation, splines, radial basis functions and several others. This includes both approximaยญ tion order and error estimates, as well as constructions of function systems for approximation of functions on Euclidean spaces and spheres. It is a piece of very good fortune that at all of the IDoMAT meetings, colยญ leagues and friends from all over Europe, and indeed some count ries outside Europe and as far away as China, New Zealand, South Africa and U.S.A. came and disยญ cussed mathematics at IDoMAT conference facility in Witten-Bommerholz. The conference was, as always, held in a friendly and congenial atmosphere. After each meeting, the delegat es were invited to contribute to the proceedยญ ing's volume, the previous one being published in the same Birkhรคuser series as this one. The editors were pleased about the quality of the contributions which could be solicited for the book. They are refereed and we should mention our gratitude to the referees and their work

CONTENT

Linear Perturbations of the Classical Orthogonal Polynomials which are Eigenfunctions of Linear Differential Operators -- (0, 1) Pรกl-type Interpolation: A General Method for Regularity -- De la Vallรฉe Poussin Means for the Hankel Transform -- Polynomial Bases on the Sphere -- A Shooting Method for Symbolic Computation of Splines -- Error Estimates for the Caratheodory-Fejรฉr Method in Polynomial Approximation -- Shape Preserving Widths of Weighted Sobolev-Type Classes -- On Approximation Methods by Using Orthogonal Polynomial Expansions -- Curious q-Series as Counterexamples in Padรฉ Approximation -- On the Degree of Approximation in Multivariate Weighted Approximation -- Semigroups Associated to Mache Operators -- A Survey on Lagrange Interpolation Based on Equally Spaced Nodes -- Multiresolution Analysis with Pulses -- H-Splines and Quasi-interpolants on a Three Directional Mesh -- Approximation by Positive Definite Kernels -- Inequalities for Polynomials With Weights Having Infinitely many Zeros on the Real Line -- Some Erd?s-type Convergence Processes in Weighted Interpolation -- Absolute Continuity of Spectral Measure for Certain Unbounded Jacobi Matrices -- Approximation on Compact Subsets of R

Mathematics
Approximation theory
Fourier analysis
Operator theory
Computer mathematics
Mathematics
Computational Mathematics and Numerical Analysis
Approximations and Expansions
Fourier Analysis
Operator Theory