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Displaying 21 – 40 of 46

Monotonicity of Harnack inequality for positive invariant harmonic functions.

Pan, Yifei, Wang, Mei (2007)

Journal of Applied Mathematics and Stochastic Analysis

On Brownian and Poissonian Convolution Semigroups on the Infinite Dimensional Torus

C. Berg (1976)

Inventiones mathematicae

On Polynomially Bounded Harmonic Functions on the $Z^{d}$ Lattice

Piotr Nayar (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

We prove that if $f : Z^{d} \to R$ is harmonic and there exists a polynomial $W : Z^{d} \to R$ such that f + W is nonnegative, then f is a polynomial.

On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold

John C. Taylor (1978)

Annales de l'institut Fourier

The Martin compactification of a bounded Lipschitz domain $D \subset R^{n}$ is shown to be $\overline{D}$ for a large class of uniformly elliptic second order partial differential operators on $D$ .Let $X$ be an open Riemannian manifold and let $M \subset X$ be open relatively compact, connected, with Lipschitz boundary. Then $\overline{M}$ is the Martin compactification of $M$ associated with the restriction to $M$ of the Laplace-Beltrami operator on $X$ . Consequently an open Riemannian manifold $X$ has at most one compactification which is a compact Riemannian...

On the Poisson integral for Lipschitz and $C^{1}$ -domains

Björn Dahlbert (1979)

Studia Mathematica

On unicity of the Riesz decomposition of an excessive measure.

Jesper Laub (1978)

Mathematica Scandinavica

Operator-valued n-harmonic measure in the polydisc

Anders Olofsson (2004)

Studia Mathematica

An operator-valued multi-variable Poisson type integral is studied. In Section 2 we obtain a new equivalent condition for the existence of a so-called regular unitary dilation of an n-tuple T=(T₁,...,Tₙ) of commuting contractions. Our development in Section 2 also contains a new proof of the classical dilation result of S. Brehmer, B. Sz.-Nagy and I. Halperin. In Section 3 we turn to the boundary behavior of this operator-valued Poisson integral. The results obtained in this section improve upon...