Fractional Differentiation Operator over an Infinite Extension of a Local Field
Functional Analysis
2007-05-23 v1 Number Theory
Probability
Abstract
We study a fractional differentiation operator for functions on the conjugate space to an infinite extension of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. In particular, a representation in the form of a hypersingular integral operator is obtained. It is also shown that the corresponding diffusion measure is not absolutely continuous with respect to the Gaussian measure.
Cite
@article{arxiv.math/9807063,
title = {Fractional Differentiation Operator over an Infinite Extension of a Local Field},
author = {Anatoly N. Kochubei},
journal= {arXiv preprint arXiv:math/9807063},
year = {2007}
}
Comments
13 pages, AMS-LaTex