29 pages, 1 figure.-- MSC2000 codes: 42C05, 33C45.-- Contributed to: XVII CEDYA: Congress on differential equations and applications/VII CMA: Congress on applied mathematics (Salamanca, Spain, Sep 24-28, 2001).MR#: MR1873645 (2002i:42031)Zbl#: Zbl 1026.42025In this contribution we summarize some new directions in the theory of orthogonal polynomials. In particular, we emphasize three kinds of orthogonality conditions which have attracted the interest of researchers from the last decade to the present time. The connection with operator theory, potential theory and numerical analysis will be shown.This work has been supported by Dirección General de Investigación (MCyT) of Spain under grant BHA2000-0206-C04-01 and INTAS project 2000-272. J...
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