Multiple orthogonal polynomials

Results on multiple orthogonal polynomials will be surveyed. Multiple orthogonal polynomials are intimately related to Hermite-Pade approximants and often they are also called Hermite-Pade polynomials. Special attention will be paid to an application of multiple orthogonal polynomials and to analytic theory of two model families of general multiple orthogonal polynomials, referred to as Angelesco and Nikishin systems. Among the applications the number theory, special functions and spectral analysis of nonsymmetric band operators will be highlighted. In the analytic theory results and methods for the study of multiple orthogonal polynomials asymptotics will be reviewed. New results on strong asymptotics of multiple orthogonal polynomials for Nikishin system will be presented. (C) 1998 Elsevier Science B.V. All rights reserved.