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Fourier transforms of powers of well-behaved 2D real analytic functions

2016/05/25 by Greenblatt, Michael
#42B20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.08089

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.

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