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Article type: Research Article
Authors: Karabegov, Alexander; *
Affiliations: Department of Mathematics, Abilene Christian University, ACU Box 28012, Abilene, TX 79699-8012, USA. E-mail: axk02d@acu.edu
Correspondence: [*] Corresponding author. E-mail: axk02d@acu.edu.
Abstract: The formal asymptotic expansion of an oscillatory integral whose phase function has one nondegenerate critical point is a formal distribution supported at the critical point which is applied to the amplitude. This formal distribution is called a formal oscillatory integral (FOI). We introduce the notion of a formal oscillatory distribution supported at a point. We prove that a formal distribution is given by some FOI if and only if it is an oscillatory distribution that has a certain nondegeneracy property. We also prove that a star product ⋆ on a Poisson manifold M is natural in the sense of Gutt and Rawnsley if and only if the formal distribution f⊗g↦(f⋆g)(x) is oscillatory for every x∈M.
Keywords: Formal oscillatory integral, oscillatory distribution, natural deformation quantization
DOI: 10.3233/ASY-201662
Journal: Asymptotic Analysis, vol. 126, no. 1-2, pp. 45-63, 2022
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