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Forum Mathematicum

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Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 30, Issue 3


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

Michael GreenblattORCID iD: http://orcid.org/0000-0001-9651-8266
Published Online: 2017-09-27 | DOI: https://doi.org/10.1515/forum-2016-0256


This paper is a companion paper to [6], where sharp estimates are proven for Fourier transforms of compactly supported functions built out of two-dimensional real-analytic functions. The theorems of [6] are stated in a rather general form. In this paper, we expand on the results of [6] 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: Fourier transform; real analytic function

MSC 2010: 42B20


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About the article

Received: 2016-12-18

Revised: 2017-04-09

Published Online: 2017-09-27

Published in Print: 2018-05-01

Citation Information: Forum Mathematicum, Volume 30, Issue 3, Pages 723–732, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2016-0256.

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