Ebook: 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.