Perturbation of Orthogonal Fourier Expansions Original Research Article

In this paper, a generalized Jacobi measure on [−1, 1] is perturbed by exponentials of functionsbof bounded mean oscillation. If we consider the Fourier series in orthogonal polynomials associated to each modification, then certain estimates (uniform inn∈N andbbelonging to some neighbourhood of the origin) are obtained. As a consequence, the partial sum operators depend analytically on the functional parameterb. The case of the Bessel series is also considered.