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Nontangential limits and Fatou-type theorems on post-critically finite self-similar sets
Fatou-type theorems post-critically finite self-similar sets
2010/11/18
In this paper we study the boundary limit properties of harmonic functions on $\mathbb R_+\times K$, the solutions $u(t,x)$ to the Poisson equation \[ \frac{\partial^2 u}{\partial t^2} + \Delta u = 0...
A Grunwald-Wang type theorem for abelian varieties
Grunwald-Wang type theorem abelian varieties
2010/12/8
Let A be an abelian variety over a number field k. We show that weak approxima-tion holds in the Weil-Chˆatelet group, H1(k,A), but that it may fail when one restricts to the n-torsion subgroup.
Muntz-type theorems on the half-line with weights
Muntz-type theorems half-line with weights
2010/12/14
We consider the linear span S of the functions tak (with some ak > 0)in weighted L2 spaces, with rather general weights. We give one necessary and one sufficient condition for S to be dense. Some comp...