Video library: I. A. Antipova, Euler--Mellin ingtegrals

VIDEO LIBRARY


International Conference on Complex Analysis Dedicated to the Memory of Andrei Gonchar and Anatoliy Vitushkin October 31, 2022 12:20, Moscow, Steklov Institute, room 910

Euler–Mellin ingtegrals I. A. Antipova Siberian Federal University, Krasnoyarsk
Abstract: Euler–Mellin integrals are multidimensional Mellin transforms of functions of the form $1/f^t$, where $f^t$ denotes the product of polynomials in complex powers, and are closely related to $A$-hypergeometric Euler type integrals. They converge and define analytic functions $M_{f}(z, t)$ in tube domains which can be given in terms of the Newton polyhedra of $f$, and the polynomials themselves are assumed to be quasi-elliptic in the sense of the definition given in [Ermolaeva–Tsikh, 1996]. According to the result of [Berkesch–Forsgard–Passare, 2014], the functions $M_{f}(z, t)$ admit a meromorphic continuation. In the talk, we discuss the details of this meromorphic continuation and alternative representations for the functions $M_{f}(z, t)$. Website: https://us06web.zoom.us/j/88002234162?pwd=dG9MbmZCbG9WVTVGUElNVW03VEM2Zz09 ^* ID: 880 0223 4162. Password: 712898