Poisson Summation Formula for The Space of Functionals

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dc.creatorNitta, Takashi
dc.creatorOkada, Tomoko
dc.date2004-05-13
dc.date.accessioned2026-07-07T05:08:12Z
dc.date.available2026-07-07T05:08:12Z
dc.descriptionIn our last work, we formulate a Fourier transformation on the infinite-dimensional space of functionals. Here we first calculate the Fourier transformation of infinite-dimensional Gaussian distribution $\exp(-πξ\int_{-\infty}^{\infty}α^2(t)dt)$ for $ξ\in{\bf C}$ with Re$(ξ)>0$, $α\in L^2({\bf R})$, using our formulated Feynman path integral. Secondly we develop the Poisson summation formula for the space of functionals, and define a functional $Z_s$, $s\in {\bf C}$, the Feynman path integral of that corresponds to the Riemann zeta function in the case Re$(s)>1$.
dc.identifierhttps://arxiv.org/abs/math/0405245
dc.identifierhttp://arxiv.org/abs/math/0405245
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71172
dc.subjectLogic
dc.subject03H05;46S20
dc.titlePoisson Summation Formula for The Space of Functionals
dc.typetext

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