La transformation de Fourier pour les ${\cal D}$-modules

“…Since S A,c is regular holonomic by a theorem of Hotta [21], it is also regular at infinity in the sense of Daia [7]. Then by using the Fourier-Sato transforms (see [28]) we can apply the main theorem of Daia [7] to get another sheaf-theoretical (or functorial) construction of the sheaf H rd n Hom D X an ((S ∨ A,c ) an , O X an ). This construction is valid even when the parameter c ∈ C n is resonant.…”

Section: ∼ −→ S ∨mentioning

confidence: 99%

Confluent A -hypergeometric functions and rapid decay homology cycles

Esterov¹,

Takeuchi²

2015

ajm

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We study confluent A-hypergeometric functions introduced by Adolphson [1]. In particular, we give their integral representations by using rapid decay homology cycles of Hien [17] and [18]. The method of toric compactifications introduced in [27] and [31] will be used to prove our main theorem. Moreover we apply it to obtain a formula for the asymptotic expansions at infinity of confluent A-hypergeometric functions.

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“…. We remark that the convention of inverse image functor in [Dai00] is different from ours. By [HTT08, Theorem 2.7.1.…”

Section: General Framework Of Euler-laplace Integral Representationmentioning

confidence: 78%

Euler and Laplace integral representations of GKZ hypergeometric functions

Matsubara-Heo¹

2019

Preprint

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We introduce an interpolation between Euler integral and Laplace integral: Euler-Laplace integral. We establish a combinatorial method of constructing a basis of the rapid decay homology group associated to Euler-Laplace integral with a nice intersection property. This construction yields a remarkable expansion formula of cohomology intersection numbers in terms of GKZ hypergeometric series. As an application, we obtain closed formulas of the quadratic relations of Aomoto-Gelfand hypergeometric functions and their confluent analogue in terms of bipartite graphs.

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La transformation de Fourier pour les ${\cal D}$-modules

Cited by 7 publications

References 15 publications

On Some Topological Properties of Fourier Transforms of Regular Holonomic -Modules

On Some Topological Properties of Fourier Transforms of Regular Holonomic -Modules

Confluent A -hypergeometric functions and rapid decay homology cycles

Euler and Laplace integral representations of GKZ hypergeometric functions

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