Mellin transforms of power-constructible functions

被引：1

作者：

Cluckers, Raf ^{[1
,2
]}

Comte, Georges ^{[3
]}

Rolin, Jean-Philippe ^{[4
]}

Servi, Tamara ^{[5
,6
]}

机构：

[1] Univ Lille, CNRS, UMR 8524, Lab Paul Painleve, F-59000 Lille, France

[2] Katholieke Univ Leuven, Dept Math, B-3001 Leuven, Belgium

[3] Univ Savoie Mont Blanc, LAMA, CNRS UMR 5127, F-73000 Chambery, France

[4] Univ Bourgogne, Inst Math Bourgogne, UMR CNRS 5584, F-21000 Dijon, France

[5] Univ Paris Cite, Inst Math Jussieu Paris Rive Gauche, CNRS, IMJ PRG, F-75013 Paris, France

[6] Sorbonne Univ, CNRS, IMJ PRG, F-75013 Paris, France

来源：

ADVANCES IN MATHEMATICS | 2024年 / 459卷

关键词：

Oscillatory integrals; Mellin transform; Fourier transform; Subanalytic functions; ASYMPTOTIC EXPANSIONS; SUBANALYTIC FUNCTIONS; INTEGRATION; SINGULARITIES; RESOLUTION; STABILITY; FIELD;

D O I：

10.1016/j.aim.2024.110025

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider several systems of algebras of real- and complex- valued functions, which appear in o-minimal geometry and related geometrically tame contexts. For each such system, we prove its stability under parametric integration and we study the asymptotics of the functions as well as the nature of their parametric Mellin transforms. (c) 2024 Published by Elsevier Inc.

引用

页数：42

共 30 条

[1] Aizenbud A, 2024, Arxiv, DOI arXiv:2403.20167
[2] [Anonymous], 2006, Quantum Field Theory. I. Basics in Mathematics and Physics: A Bridge Between Mathematicians and Physicists
[3] Arnold V.I., 1988, Monographs in Mathematics, V83
[4] RESOLUTION OF SINGULARITIES AND DIVISION OF DISTRIBUTIONS
ATIYAH, MF
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1970, 23 (02) : 145 - &
[5] TAME TOPOLOGY OF ARITHMETIC QUOTIENTS AND ALGEBRAICITY OF HODGE LOCI
Bakker, B.
Klingler, B.
Tsimerman, J.
[J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2020, 33 (04) : 917 - 939
[6] Cluckers R, 2023, Arxiv, DOI arXiv:2308.15958
[7] INTEGRATION OF OSCILLATORY AND SUBANALYTIC FUNCTIONS
Cluckers, Raf
Comte, Georges
Miller, Daniel J.
Rolin, Jean-Philippe
Servi, Tamara
[J]. DUKE MATHEMATICAL JOURNAL, 2018, 167 (07) : 1239 - 1309
[8] Loci of Integrability, Zero Loci, and Stability Under Integration for Constructible Functions on Euclidean Space with Lebesgue Measure
Cluckers, Raf
Miller, Daniel J.
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2012, 2012 (14) : 3182 - 3191
[9] STABILITY UNDER INTEGRATION OF SUMS OF PRODUCTS OF REAL GLOBALLY SUBANALYTIC FUNCTIONS AND THEIR LOGARITHMS
Cluckers, Raf
Miller, Daniel J.
[J]. DUKE MATHEMATICAL JOURNAL, 2011, 156 (02) : 311 - 348
[10] Log-analytic nature of the volume of subanalytic sets
Comte, G
Lion, JM
Rolin, JP
[J]. ILLINOIS JOURNAL OF MATHEMATICS, 2000, 44 (04) : 884 - 888

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