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Title: An algorithmic study on the integration of holonomic hyperfunctions - oscillatory integrals and a phase space integral associated with a Feynman diagram (New development of microlocal analysis and singular perturbation theory)
Authors: Oaku, Toshinori
Keywords: 14F10
42B20
81Q30
holonomic system
hyperfunction
algorithm
oscillatory integral
Feynman integral
Issue Date: Jun-2019
Publisher: Research Institute for Mathematical Sciences, Kyoto University
Journal title: 数理解析研究所講究録別冊 = RIMS Kokyuroku Bessatsu
Volume: B75
Start page: 41
End page: 60
Abstract: Let u(x, y) be a generalized function which satisfies a holonomic system M of linear differential equations with polynomial coefficients. Suppose that u(x, y) is integrable with respect to x and let v(y) be its integral. We give asufficient condition for v(y) to satisfy the D - module theoretic integration module of M, which can be computed algorithmically. We present some examples related to oscillatory integrals and Cutkosky - type phase space integrals associated with Feynman diagrams
Description: "New development of microlocal analysis and singular perturbation theory". October 3-7, 2016. edited by Naofumi Honda and Yasunori Okada. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.
Rights: © 2019 by the Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.
URI: http://hdl.handle.net/2433/244770
Appears in Collections:B75 New development of microlocal analysis and singular perturbation theory

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