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arXiv · 1407.8308

Mittag-Leffler Analysis I: Construction and characterization

Martin Grothaus·Florian Jahnert·Felix Riemann·José Luís da Silva
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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.

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Martin Grothaus, Florian Jahnert, Felix Riemann, José Luís da Silva. 2014-07-31. Mittag-Leffler Analysis I: Construction and characterization. https://doi.org/10.1016/j.jfa.2014.12.007

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