Interpolation in spaces of harmonic functions with asymptotic expansions.

Gaspar Mora Martínez

Collectanea Mathematica (1989)

  • Volume: 40, Issue: 3, page 277-287
  • ISSN: 0010-0757

Abstract

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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.

How to cite

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Mora Martínez, Gaspar. "Interpolación en espacios de funciones armónicas con desarrollos asintóticos.." Collectanea Mathematica 40.3 (1989): 277-287. <http://eudml.org/doc/41793>.

@article{MoraMartínez1989,
author = {Mora Martínez, Gaspar},
journal = {Collectanea Mathematica},
keywords = {Funciones diferenciables; Función armónica},
language = {spa},
number = {3},
pages = {277-287},
title = {Interpolación en espacios de funciones armónicas con desarrollos asintóticos.},
url = {http://eudml.org/doc/41793},
volume = {40},
year = {1989},
}

TY - JOUR
AU - Mora Martínez, Gaspar
TI - Interpolación en espacios de funciones armónicas con desarrollos asintóticos.
JO - Collectanea Mathematica
PY - 1989
VL - 40
IS - 3
SP - 277
EP - 287
LA - spa
KW - Funciones diferenciables; Función armónica
UR - http://eudml.org/doc/41793
ER -

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