Submission date: 9 March 2017

Abstract:

We study upper bounds, approximations, and limits for functions of motivic exponential class, uniformly in non-Archimedean local fields whose characteristic is 0 or sufficiently large. Our results together form a flexible framework for doing analysis over local fields in a field-independent way. As corollaries, we obtain many new transfer principles, for example, for local constancy, continuity, and existence of various kinds of limits. Moreover, we show that the Fourier transform of an L^2-function of motivic exponential class is again of motivic exponential class. As an application in the realm of representation theory, we prove uniform bounds for the normalized by the discriminant Fourier transforms of orbital integrals on connected reductive p-adic groups.

Mathematics Subject Classification: 14E18 (primary), 22E50, 40J99

Keywords and phrases:

Full text arXiv 1703.03381: pdf, ps.