7 research outputs found
Polynomial Growth Harmonic Functions on Finitely Generated Abelian Groups
Full text linkIn the present paper, we develop geometric analytic techniques on Cayley
graphs of finitely generated abelian groups to study the polynomial growth
harmonic functions. We develop a geometric analytic proof of the classical
Heilbronn theorem and the recent Nayar theorem on polynomial growth harmonic
functions on lattices \mathds{Z}^n that does not use a representation formula
for harmonic functions. We also calculate the precise dimension of the space of
polynomial growth harmonic functions on finitely generated abelian groups.
While the Cayley graph not only depends on the abelian group, but also on the
choice of a generating set, we find that this dimension depends only on the
group itself.Comment: 15 pages, to appear in Ann. Global Anal. Geo
Uniform Boundedness and Long-Time Asymptotics for the Two-Dimensional Navier–Stokes Equations in an Infinite Cylinder
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Varietes riemanniennes isometriques a l'infini
No full textSIGLEAvailable at INIST (FR), Document Supply Service, under shelf-number : 22522, issue : a.1994 n.04 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc
