Formal oscillatory distributions
Keyword(s):
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.
2015 ◽
Vol 2015
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pp. 1-6
1985 ◽
Vol 27
(2)
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pp. 245-257
2001 ◽
Vol 70
(3)
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pp. 351-386
1998 ◽
Vol 221
(2)
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pp. 658-671
2001 ◽
Vol 73
(2)
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pp. 191-196
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1965 ◽
Vol 54
(6)
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pp. 1759-1763
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1989 ◽
Vol 426
(1871)
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pp. 273-286
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