Perturbation of orthogonal Fourier expansions

In this paper. a generalized Jacobi measure on [-1, 1] is perturbed by exponentials of functions b of bounded mean oscillation. If we consider the Fourier series in orthogonal polynomials associated to each modification, then certain estimates (uniform in n is an element of N and b belonging to some neighbourhood of the origin) are obtained. As a consequence, the partial sum operators depend analytically on the functional parameter b. The case of the Bessel series is also considered. (C) 1998 Academic Press.