The article puts up the problem of finding harmonic functions on a domain D, which for simplicity is a disk with the origin as a boundary point, continuous on D, and with arbitrary asymptotic harmonic expansion. To solve it, in the space Ac(D) of harmonic functions on D, continuous on D and with aymptotic harmonic expansion at 0, we define the topology Tc for which it is a Fréchet space. There we define the linear functionals which map each function to the coefficients of its asymptotic harmonic expansion. Let b be the linear span of these functionals; if lambda denotes the topology of uniform convergence on the compacts of Ac(D), we have that b is a Silva space and lambda coincides with the topology U, inductive limit of finite dimensional subspaces. These relations and the Hahn-Banach theorem lead us to solve the problem.
@article{urn:eudml:doc:41793,
title = {Interpolaci\'on en espacios de funciones arm\'onicas con desarrollos asint\'oticos.},
journal = {Collectanea Mathematica},
volume = {40},
year = {1989},
pages = {277-287},
zbl = {0742.30035},
mrnumber = {MR1099245},
language = {es},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41793}
}
Mora Martínez, Gaspar. Interpolación en espacios de funciones armónicas con desarrollos asintóticos.. Collectanea Mathematica, Tome 40 (1989) pp. 277-287. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41793/