Multivariate Approximation Theory III : Proceedings of the Conference at the Mathematical Research Institute at Oberwolfach, Black Forest, January 20–26, 1985

Zur Tagung -- List of Participants -- Program of the Sessions -- L. Bamberger: Interpolation in bivariate spline spaces -- n-th order polynomial spline blending -- The limits of multivariate cardinal splines -- Local smoothing for scattered and noisy data -- Convexity and variation diminishing property of Bernstein polynomials over triangles -- The dimensions of bivariate spline spaces over triangulations -- On bivariate vertex splines -- Biorthogonal system of polynomials on the standard simplex -- Anwendung der Approximationstheorie auf gewisse singulare Randwertaufgaben -- Combinatorial aspects of multivariate splines -- Intermediate blending interpolation -- Hermite-interpolation in N variables and minimal cubature formulae -- Some reflections on multi-dimensional Euler and Poisson summation formulas -- On the dimension of the spline space S 21(D) in special cases -- Degree of best approximation by blending functions -- Shape preserving approximation by polyhedral splines -- Numerical realization of boundary collocation methods -- Interpolation by polynomials and natural splines on normal lattices -- Bivariate approximation procedures -- Construction and applications of Hermite interpolating quadratic spline functions of two and three variables -- Hermite-Fejér and higher Hermite-Fejér interpolation with boundary conditions -- Some uniqueness problems in best Chebyshev and mean multivariate approximation -- Minimal projections in tensor product spaces -- Convergence of Hermite-Fejér interpolation via Korovkin's theorem -- Cubature error bounds using degrees of approximation -- Square functions in the theory of Cesaro summability of double orthogonal series -- Generalized Melkes interpolation -- Approximation theory and analysis of spectral methods -- On multivariate polynomial L1-approximation to zero and related coefficient inequalities -- Abschatzungen von Lagrange-Quadratsummen für die Sphäre mit Hilfe gewisser Eigenwerte -- On Gabor information cells -- Ein Beitrag zur Flachenapproximation über unregelmäßig vertei lten Daten -- The basis and moment problems of some systems of analytic functions -- Normen von Projektionen in mehreren Veranderlichen -- The solution of generalized least squares problems.;The Fourth International Symposium on Multivariate Approximation Theory was held at the Oberwolfach Mathematical Research Insti­ tute, Black Forest, W.-Germany, during the week of January 20 - 26, 1985. The preceding conferences on this topic were held in 1976, 1979, and 1982 \* . We were pleased to have more than 50 mathematicians from 13 countries in attendance. The program in­ cluded 40 lectures. These Proceedings form a record of most of the papers presented at the Symposium. The topics treated cover different problems on multivariate approximation such as polynomial approximation on simplices, multivariate splines (box-splines, dimension of spline spaces), blending methods, multivariate Hermite interpolation, data smoothing and surface representation, and multivariate summation methods. We would like to thank the director of the Oberwolfach Mathe­ matical Research Institute, Prof. Dr. M. Barner, and his staff for providing the facilities. Of the people who gave their time to help make this conference a success, we would like to mention in particular Prof. Dr. F.J. Delvos (Siegen), Dr. G. Baszenski (College Station, Texas), and Dipl.-Math. H. Nienhaus (Siegen). Finally, our thanks are due to Carl Einsele of Birkhauser Publishers for his valuable cooperation. Front Matter....Pages 1-23 Zur Tagung....Pages 11-11 List of Participants....Pages 13-17 Program of the Sessions....Pages 19-23 Interpolation in Bivariate Spline Spaces....Pages 25-34 n -th Order Polynomial Spline Blending....Pages 35-46 The Limits of Multivariate Cardinal Splines....Pages 47-50 Local Smoothing for Scattered and Noisy Data....Pages 51-60 Convexity and Variation Diminishing Property of Bernstein Polynomials over Triangles....Pages 61-70 The Dimensions of Bivariate Spline Spaces Over Triangulations....Pages 71-83 On Bivariate Vertex Splines....Pages 84-115 Biorthogonal System of Polynomials on the Standard Simplex....Pages 116-119 Anwendung der Approximationstheorie auf gewisse singulare randwertaufgaben....Pages 120-129 Combinatorial Aspects of Multivariate Splines....Pages 130-137 Intermediate blending Interpolation....Pages 138-153 Hermite-Interpolation in N Variables and Minimal Cubature Formulae....Pages 154-165 Some Reflections on Multidimensional Euler and Poisson Summation Formulas....Pages 166-179 Degree of Best Approximation by Blending Functions....Pages 180-190 Shape Preserving Approximation by Polyhedral Splines....Pages 191-197 Numerical Realization of Boundary Collocation Methods....Pages 198-205 Interpolation by Polynomials and Natural Splines on Normal Lattices....Pages 206-217 Bivariate Approximation Procedures....Pages 218-220 Construction and Applications of Hermite Interpolating Quadratic Spline Functions of two and three Variables....Pages 221-231 Hermite-Fejer and Higher Hermite-Fejer Interpolation with Boundary Conditions....Pages 232-252 Some uniqueness problems in best Chebyshev and mean multivariate approximation....Pages 253-261 Minimal Projections in Tensor Product Spaces....Pages 262-269 Convergence of Hermite-Fejér Interpolation via Korovkin’s Theorem....Pages 270-276 Cubature Error Bounds using Degrees of Approximation....Pages 277-285 Square Functions in the Theory of Cesàro Summability of Double Orthogonal Series....Pages 286-297 Generalized Melkes Interpolation....Pages 298-308 Approximation Theory and Analysis of Spectral Methods....Pages 309-321 On Multivariate Polynomial L 1 — Approximation to Zero and Related Coefficient Inequalities....Pages 322-331 Abschätzungen von Lagrange-Quadratsummen für die Sphäre mit Hilfe gewisser Eigenwerte....Pages 332-342 On Gabor Information Cells....Pages 343-348 Ein Beitrag zur Flächenapproximation über Unregelmässig Verteilten Daten....Pages 349-362 The Basis and Moment Problems of some Systems of Analytic Functions....Pages 363-369 Normen von Projektionen in Mehreren Veränderlichen....Pages 370-379 The Solution of Generalized Least Squares Problems....Pages 380-387 ....Pages 388-400