Functions of locally bounded variation on Wiener spaces

We introduce the concept of functions of locally bounded variation on abstract Wiener spaces and study their properties. Some nontrivial examples and applications to stochastic analysis are also discussed.Comment: 20 pages, accepted for publicatio

Structure functions in polarized proton-deuteron Drell-Yan processes

Polarized proton-deuteron (pd) Drell-Yan processes are investigated for studying new spin structure of a spin-1 hadron. Our formalism indicates that there exist many structure functions: 108 in general and 22 in the \vec Q_T-integrated case. A naive parton model suggests that at least one of them should be related to the tensor polarized distributions, which have not been measured at all. There are some experimental possibilities at FNAL, HERA, and RHIC to study the polarized pd reactions.Comment: 1+3 pages, LaTeX, espcrc2.sty. Talk at the 7th international workshop on Deep Inelastic Scattering and QCD, Zeuthen, Germany, April 19-23, 1999. To be published in Nucl. Phys. B. Complete postscript file is available at http://www2.cc.saga-u.ac.jp/saga-u/riko/physics/quantum1/structure.html Email: [email protected]

Fractional order Taylor's series and the neo-classical inequality

We prove the neo-classical inequality with the optimal constant, which was conjectured by T. J. Lyons [Rev. Mat. Iberoamericana 14 (1998) 215-310]. For the proof, we introduce the fractional order Taylor's series with residual terms. Their application to a particular function provides an identity that deduces the optimal neo-classical inequality.Comment: 11 pages, 1 figur

Proton-deuteron asymmetry in Drell-Yan processes and polarized light-antiquark distributions

We discuss the relation between the ratio of the proton-deuteron (pd) Drell-Yan cross section to the proton-proton (pp) one \Delta_{(T)} \sigma_{pd}/2 \Delta_{(T)} \sigma_{pp} and the flavor asymmetry in polarized light-antiquark distributions. Using a recent formalism of the polarized pd Drell-Yan process, we show that the difference between the pp and pd cross sections is valuable for finding not only the flavor asymmetry in longitudinally polarized antiquark distributions but also the one in transversity distributions. It is especially important that we point out the possibility of measuring the flavor asymmetry in the transversity distributions because it cannot be found in W production processes and inclusive lepton scattering due to the chiral-odd property.Comment: 10 pages, LATEX2e with epsfig.sty, 4 eps figures. Complete postscript file including the figures is available at http://www-hs.phys.saga-u.ac.jp . Email: [email protected], [email protected]

Dirichlet spaces on H-convex sets in Wiener space

We consider the $(1,2)$-Sobolev space $W^{1,2}(U)$ on subsets $U$ in an abstract Wiener space, which is regarded as a canonical Dirichlet space on $U$. We prove that $W^{1,2}(U)$ has smooth cylindrical functions as a dense subset if $U$ is $H$-convex and $H$-open. For the proof, the relations between $H$-notions and quasi-notions are also studied.Comment: 18 pages, 1 figure. Erratum has been added, which was accepted for publication in Bull. Sci. Mat