Discrete harmonic analysis associated with Jacobi expansions

Abstract

The study of the classical harmonic analysis operators in non-trigonometric contexts has a very rich history and it has been widely addressed in the continuous setting. However, the situation in the discrete one is totally opposed. In spite of several works in the discrete setting (v.g. [5]), there was a lack of them in non-trigonometric contexts until the paper by J. J. Betancor et al. [4], where the ultraspherical orthonormal system is considered. In this talk, we extend that work and we present the study of classical Harmonic Analysis operators associated with Jacobi expansions.