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- W2974661810 abstract "With $(X,mathfrak{d},mathfrak{m})$ an $mathrm{RCD}^*(K,N)$ space for some $Kinmathbf{R}$, $Nin [1,infty)$, let $H$ be the self-adjoint Laplacian induced by the underlying Cheeger form. Given $alphain [0,1]$ we introduce the $alpha$-Kato class of potentials on $(X,mathfrak{d},mathfrak{m})$, and given a potential $V:Xto mathbf{R}$ in this class, with $H_V$ the natural self-adjoint realization of the Schrodinger operator $H+V$ in $L^2(X,mathfrak{m})$, we use Brownian coupling methods and perturbation theory to prove that for all $t>0$ there exists an explicitly given constant $A(V,K,alpha,t)<infty$, such that for all $Psiin L^{infty}(X,mathfrak{m})$, $x,yin X$ one has begin{align*} big|e^{-tH_V}Psi(x)-e^{-tH_V}Psi(y)big|leq A(V,K,alpha,t) |Psi|_{L^{infty}}mathfrak{d}(x,y)^{alpha}. end{align*} In particular, all $L^{infty}$-eigenfunctions of $H_V$ are globally $alpha$-Holder continuous. This result applies to multi-particle Schrodinger semigroups and, by the explicitness of the Holder constants, sheds some light into the geometry of such operators." @default.
- W2974661810 created "2019-09-26" @default.
- W2974661810 creator A5020400774 @default.
- W2974661810 date "2019-09-17" @default.
- W2974661810 modified "2023-09-27" @default.
- W2974661810 title "$mathrm{RCD}^*(K,N)$ spaces and the geometry of multi-particle Schrodinger semigroups" @default.
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