On a Finite Range Decomposition of the Resolvent of a Fractional Power of the Laplacian II. The Torus - Laboratoire Charles Coulomb (L2C) Accéder directement au contenu
Article Dans Une Revue Journal of Statistical Physics Année : 2017

On a Finite Range Decomposition of the Resolvent of a Fractional Power of the Laplacian II. The Torus

Pronob Mitter
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Résumé

In previous papers, [M1, M2], [M3], we proved the existence as well as regularity of a finite range decomposition for the resolvent $G_{\alpha} (x-y,m^2) = ((-\Delta)^{\alpha\over 2} + m^{2})^{-1} (x-y) $, for $0<\alpha <2$ and all real $m$, in the lattice ${\bf Z}^{d}$ for dimension $d\ge 2$. In this paper, which is a continuation of the previous one, we extend those results by proving the existence as well as regularity of a finite range decomposition for the same resolvent but now on the lattice torus ${\bf Z}^{d}/L^{N+1}{\bf Z}^{d} $ for $d\ge 2$ provided $m\neq 0$ and $0<\alpha <2$. We also prove differentiability and uniform continuity properties with respect to the resolvent parameter $m^{2}$. Here $L$ is any odd positive integer and $N\ge 2$ is any positive integer.

Dates et versions

hal-01492858 , version 1 (20-03-2017)

Identifiants

Citer

Pronob Mitter. On a Finite Range Decomposition of the Resolvent of a Fractional Power of the Laplacian II. The Torus. Journal of Statistical Physics, 2017, 168 (5), pp.986-999. ⟨10.1007/s10955-017-1828-5⟩. ⟨hal-01492858⟩
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