Titolo della tesi: Infinite Dimensional Analysis through Special Functions and Generalized Fractional Operators
Motivated by the results of white noise and especially Mittag-Leffler analysis, we first construct two non-Gaussian settings defined through upper-incomplete gamma function and generalized Wright functions, respectively. In both cases, we introduce the related Appell system and the spaces of test functions, as well as the distributions’ space. In the case of generalized Wright analysis, we study the Donsker’s delta and prove the existence of local times. In the second part, we introduce the so called Bernstein Gaussian processes, by defining general fractional operators and applying these in the white noise setting. By using the tools of white noise analysis, we prove the existence of the related noise and of the Ornstein-Uhlenbeck process.