UNIFORMLY ELLIPTIC-OPERATORS ON AN INFINITE DIMENSIONAL TORUS

In this note we present some Gaussian-type estimates on the heat kernel for the differential operator H = SIGMA1 infinity partial derivative(i)(a(ij)(x)partial derivative(j)) on the compact Abelian group T(infinity). These estimates we apply to investigate the sheaves H and H of harmonic functions generated by the operators H and H=partial derivative(t) + H.