Fourier transforms of powers of well-behaved 2D real analytic functions
Classical Analysis and ODEs
2016-05-27 v1
Abstract
This paper is a companion paper to [G4], where sharp estimates are proven for Fourier transforms of compactly supported functions built out of two-dimensional real-analytic functions. The theorems of [G4] are stated in a rather general form. In this paper, we expand on the results of [G4] and show that there is a class of "well-behaved" functions that contains a number of relevant examples for which such estimates can be explicitly described in terms of the Newton polygon of the function. We will further see that for a subclass of these functions, one can prove noticeably more precise estimates, again in an explicitly describable way.
Keywords
Cite
@article{arxiv.1605.08089,
title = {Fourier transforms of powers of well-behaved 2D real analytic functions},
author = {Michael Greenblatt},
journal= {arXiv preprint arXiv:1605.08089},
year = {2016}
}
Comments
13 pages