Tohoku Mathematical Journal
2022
December
SECOND SERIES VOL. 74, NO. 4

Tohoku Math. J.
74 (2022), 501-520

Title STOKES MATRICES FOR AIRY EQUATIONS

Author Andreas Hohl and Konstantin Jakob

(Received April 7, 2021, revised April 30, 2021)
Abstract. We compute Stokes matrices for generalised Airy equations and prove that they are regular unipotent (up to multiplication with the formal monodromy). This class of differential equations was defined by Katz and includes the classical Airy equation. In addition, it includes differential equations which are not rigid. Our approach is based on the topological computation of Stokes matrices of the enhanced Fourier--Sato transform of a perverse sheaf due to D'Agnolo, Hien, Morando and Sabbah.

Mathematics Subject Classification. Primary 34M40; Secondary 33C20, 44A10.
Key words and phrases. Airy equations, hypergeometric equations, Stokes phenomenon, Fourier--Laplace transform.

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