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)

"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.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 diagram