This book contains the refereed papers which were presented at the second In ternational Dortmund Meeting on Approximation Theory (IDoMAT 98) at Haus Bommerholz, the conference center of Dortmund University, during the week of February 23-27,1998. At this conference 52 researchers and specialists from Bul garia, China, France, Great Britain, Hungary, Israel, Italy, Roumania, South Africa and Germany participated and described new developments in the fields of uni variate and multivariate approximation theory. The papers cover topics such as radial basis functions, bivariate spline interpolation, multilevel interpolation, mul tivariate triangular Bernstein bases, Pade approximation, comonotone polynomial approximation, weighted and unweighted polynomial approximation, adaptive ap proximation, approximation operators of binomial type, quasi interpolants, gen eralized convexity and Peano kernel techniques. This research has applications in areas such as computer aided geometric design, as applied in engineering and medical technology (e. g. computerised tomography). Again this international conference was wholly organized by the Dortmund Lehrstuhl VIII for Approximation Theory. The organizers attached great impor tance to inviting not only well-known researchers but also young talented math ematicians. IDoMAT 98 gave an excellent opportunity for talks and discussions between researchers from different fields of Approximation Theory. In this way the conference was characterized by a warm and cordial atmosphere. The success of IDoMAT 98 was above all due to everyone of the participants."

The current form of modern approximation theory is shaped by many new de velopments which are the subject of this series of conferences. The International Meetings on Approximation Theory attempt to keep track in particular of fun damental advances in the theory of function approximation, for example by (or thogonal) polynomials, (weighted) interpolation, multivariate quasi-interpolation, splines, radial basis functions and several others. This includes both approxima 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, col 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 dis 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 proceed ing's volume, the previous one being published in the same Birkhauser 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."

Feller Semigroups, Bernstein type Operators and Generalized Convexity Associated with Positive Projections.- Gregory's Rational Cubic Splines in Interpolation Subject to Derivative Obstacles.- Interpolation by Splines on Triangulations Oleg Davydov.- On the Use of Quasi-Newton Methods in DAE-Codes.- On the Regularity of Some Differential Operators.- Some Inequalities for Trigonometric Polynomials and their Derivatives.- Inf-Convolution and Radial Basis Functions.- On a Special Property of the Averaged Modulus for Functions of Bounded Variation.- A Simple Approach to the Variational Theory for Interpolation on Spheres.- Constants in Comonotone Polynomial Approximation - A Survey.- Will Ramanujan kill Baker-Gammel-Wills? (A Selective Survey of Pade Approximation).- Approximation Operators of Binomial Type.- Certain Results involving Gammaoperators.- Recent research at Cambridge on radial basis functions.- Representation of quasi-interpolants as differential operators and applications.- Native Hilbert Spaces for Radial Basis Functions I.- Adaptive Approximation with Walsh-similar Functions.- Dual Recurrence and Christoffel-Darboux-Type Formulas for Orthogonal Polynomials.- On Some Problems of Weighted Polynomial Approximation and Interpolation.- Asymptotics of derivatives of orthogonal polynomials based on generalized Jacobi weights. Some new theorems and applications.- List of participants.