2020/06/02 by Alexander Karabegov, Karabegov, Alexander
Mathematics · #53D55 #81Q20 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:53D55 #msc:81Q20
paper · pdf · doi:10.48550/arxiv.2006.01692
20 pages, several typos were corrected
arxiv created 2020/06/08 · arxiv updated 2020/06/11
We introduce the notion of an oscillatory formal distribution supported at a point. We prove that a formal distribution is given by a formal oscillatory integral if and only if it is an oscillatory distribution that has a certain nondegeneracy property. We give an algorithm that recovers the jet of infinite order of the integral kernel of a formal oscillatory integral at the critical point from the corresponding formal distribution. 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.