Mittag-Leffler Analysis I: Construction and characterization
Functional Analysis
2017-08-23 v1
Abstract
We construct an infinite dimensional analysis with respect to non-Gaussian measures of Mittag-Leffler type which we call Mittag-Leffler measures. It turns out that the well-known Wick ordered polynomials in Gaussian analysis cannot be generalized to this non-Gaussian case. Instead of using Wick ordered polynomials we prove that a system of biorthogonal polynomials, called Appell system, is applicable to the Mittag-Leffler measures. Therefore we are able to introduce a test function and a distribution space. As an application we construct Donsker's delta in a non-Gaussian setting as a weak integral in the distribution space.
Cite
@article{arxiv.1407.8308,
title = {Mittag-Leffler Analysis I: Construction and characterization},
author = {Martin Grothaus and Florian Jahnert and Felix Riemann and José Luís da Silva},
journal= {arXiv preprint arXiv:1407.8308},
year = {2017}
}