Functional Analysis and Approximation Theory V, Proceedings of the 5th International Conference on Functional Analysis and Approximation Theory held in Acquafredda di Maratea (Potenza), June 16 – 23, 2004,

During the week of September 16 - 23, 2004, the Fifth International Conference on Functional Analysis and Approximation Theory was held at Acquafredda di Maratea (Potenza). Earlier meetings were held in 1989, 1992, 1996 and 2000 at the same place. The Conference was organized by the Center for Studies on Functional Analysis and Approximation Theory of the University of Basilicata (Potenza), directed by Prof. Giuseppe Mastroianni, with the collaboration of the National Research Group “Operator Theory, Semigroups and Applications to Evolution Equations and Approximation Problems”(PRIN – COFIN 2003-2005), directed by Prof. Francesco Altomare. Besides Francesco Altomare and Giuseppe Mastroianni, the organizing committee consisted also of Antonio Attalienti, Michele Campiti, Lorenzo D’Ambrosio, Sabrina Diomede, Donatella Occorsio and Maria Grazia Russo. The scientific committee consisted of Francesco Altomare, Antonio Attalienti, Michele Campiti, Romulus Cristescu, Giuseppe Mastroianni, Ioan Raşa, József Szabados and Peter Vertesi, The meeting was devoted to some significant aspects of contemporary mathematical research on Functional Analysis, Operator Theory and Approximation Theory including the applications of these fields in other areas such as partial differential equations, integral equations, numerical analysis and stochastic analysis. A special session was dedicated to Professor Giuseppe Mastroianni on the occasion of his 65th birthday, as a fair token of gratitude for his contribution to mathematics and to the organization of all the Maratea conferences (1989 – 2004). The Conference was attended by over 180 mathematicians coming from 25 countries. The scientific program consisted of 15 plenary lectures, 4 joint section talks and about 130 communications. Several thematic sessions were arranged. Among the main topics treated therein we mention: - Banach spaces, approximation in normed spaces. - Function spaces and approximation problems. - Linear operators on Banach spaces. Positive operators. Spectral theory. - Semigroups of operators, Feller semigroups and partial differential equations. Maximal regularity. Stochastic analysis. - Real functions and inequalities. Complex approximation. - Approximation by polynomials. Best approximation. - Approximation by positive operators. Rate of convergence. - Orthogonal polynomials. - Integral equations. - Interpolation and quadrature formulas. - Integral operators, integral transforms and Fourier integrals. - Wavelets and signal processing. - Numerical analysis and stability 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: • Department of Mathematics of the University of Basilicata (Potenza), • Department of Mathematics of the University of Bari, • Department of Economics of the University of Bari, • Department of Mathematics of the University of Lecce, • Faculty of Sciences of the University of Basilicata, • University of Basilicata, • University of Bari, • National Group for Mathematical Analysis, Probability and their Applications (G.N.A.M.P.A.), • Basilicata Region Administration, • Basilicata Tourism Board. We are particularly indebted to Mirella Cappelletti Montano, Carmela De Bonis, Vita Leonessa, Sabina Milella, Graziana Musceo and Gabriella Sabino, who assisted and helped us in organizing the Conference secretariat services. To all of them we express our special thanks. We are also grateful to Biancamaria Della Vecchia for her friendly collaboration. Finally we would like to thank Professor P. Vetro for accepting to publish the Proceedings of the Conference in a supplement of "Rendiconti del Circolo Matematico di Palermo". May 2005 Francesco Altomare On behalf of the Organizing Committee