Orthogonal polynomials and cubic polynomial mappings (I)

29 pages, no figures.-- MSC1991 code: Primary 42C05.MR#: MR1789676 (2001m:42047)We present characterization theorems for orthogonal polynomials obtained from a given system of orthogonal polynomials by a cubic polynomial transformation in the variable. Since such polynomials are the denominators of the approximants for the expansion in continued fractions of the x-transform of the moment sequences associated with the linear functionals with respect to which such polynomials are orthogonal, we state the explicit relation for the corresponding formal Stieltjes series. As an application, we study the eigenvalues of a tridiagonal 3-Toeplitz matrix. Finally, we deduce the second-order linear differential equation satisfied by the new family of orthogonal polynomials when the initial family satisfies such a kind of differential equation.The work of the first author was supported by Dirección General de Enseñanza Superior (DGES) of Spain under grant PB96-0120-C03-01 and INTAS program, INTAS-93-0219 Ext. The work of the second author was supported by Junta Nacional de Investigação Científica e Tecnológica (JNICT) under grant BD976 and Centro de Matemática da Universidade de Coimbra (CMUC) of Portugal.Publicad