Interpolación en espacios de funciones armónicas con desarrollos asintóticos

• Autores: Gaspar Mora Martínez
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 40, Fasc. 3, 1989, págs. 277-287
• Idioma: español
• Títulos paralelos:
  • Interpolation in spaces of harmonic functions with asymptotic expansions
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• Resumen

  • 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.