Functional Analysis and Approximation Theory IV, Proceedings of the 4th International Conference on Functional Analysis and Approximation Theory held in Acquafredda di Maratea (Potenza), September 22 - 28, 2000

During the week of September 22 - 28, 2000, the Fourth International Conference on Functional Analysis and Approximation Theory was held at Acquafredda di Maratea (Potenza). Earlier meetings were held in 1989, 1992 and 1996 at the same location. The Conference was organized by the Center for Studies on Functional Analysis and Approximation Theory of the University of Basilicata (Potenza), which is directed by Prof. Giuseppe Mastroianni, with the collaboration of the Department of Mathematics of the University of Basilicata and the Department of Mathematics of the University and the Polytechnic of Bari. Besides Giuseppe Mastroianni, the executive organizing committee consisted also of Francesco Altomare, Antonio Attalienti, Michele Campiti, Bianca Maria Della Vecchia and Mario Rosario Occorsio. The main aim of the Conference was to promote interactions between specialists and young researchers in Functional Analysis and Approximation Theory as well as to renew some stimulations in solving several related open problems and in showing applications to other fields of Mathematics closer to the applied sciences. The Conference was attended by over 160 mathematicians coming from 22 countries. The programme included 15 invited lectures and over 100 research talks. Among the main topics treated therein we mention: - Banach spaces, Banach algebras, Fréchet spaces, approximation in normed spaces. Best approximation. - Function spaces and approximation problems. - Linear operators on Banach spaces, spectral theory, ergodic theory, positive operators, algebraic systems of operators. - Groups and semigroups of operators, Feller semigroups, evolution equations. - Real functions and inequalities. Complex approximation. - Approximation by positive operators. Rate of convergence. - Orthogonal polynomials and Padé approximation. - Integral equations. - Interpolation and quadrature formulas. - Integral transforms and Fourier series. - Wawelets and digital information processing. - Numerical analysis and stability methods. In this volume we collect some invited lectures together with a selection of the papers corresponding to the research talks, which have been carefully refereed. Our thanks go to the referees for their collaboration as well as for their accurate work. We gratefully acknowledge the financial support of the Institutions listed below: - Directorate General for Cultural Promotion and Cooperation for the Ministry of Foreign Affairs - National Group for Mathematical Analysis, Probability and their Applications (G.N.A.M.P.A.) - National Project on Functional Analysis (M.U.R.S.T.) - University of Basilicata - University of Bari - Polytechnic of Bari - Department of Mathematics of the University of Basilicata - Department of Mathematics of the University and of the Polytechnic of Bari - Basilicata Tourism Board. We are particularly indebted to Giuseppe Colacicco and Lorenzo D’Ambrosio who assisted and helped us in organizing the Conference secretariat services. To both of them we express our special thanks. Finally we would like to thank Professor P. Vetro and the Editorial Board of the Journal "Rendiconti del Circolo Matematico di Palermo" for accepting to publish the Proceedings of the Conference in two supplements of the same Journal. December 2001 THE ORGANIZING COMMITTEE