Zeta regularized integral and Fourier expansion of functions on an infinite dimensional torus

摘要

Let {H, G} be a pair of a Hilbert space and a Schatten class operator G suchthat ζ(G, s) = trG~sis holomorphic ats =0. Then regularization of integralson suitable subsets of H~#,an extension ofHobtained to add a 1-dimensionalspace, is defined by using ζ(G, s).In this paper, we apply regularizedintegral to periodic functions of H~#, and show practical computations of Fourierexpansions of periodic functions. Results also show there exists de Rham typecohomology having the Poincare duality exists on suitable infinite dimensionaltorus.