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...
En este artículo revisamos un famoso teorema, descubierto por H. Steinhaus en 1936, en el que se da una condición suficiente que permite obtener las funciones coordenadas de una curva que llena el cuadrado unidad. Ponemos de manifiesto que el recíproco de este teorema no se cumple para la curva de Lebesgue. Aquí proponemos un teorema de caracterización de curvas que llenan el espacio, basado en una condición de llenado. Asimismo, damos una caracterización constructiva de esta condición de llenado...
The systems of an arbitrary number of linear inequalities OVer a real locally convex space have been classified in three classes, namely: consistent, weakly inconsistent and strongly inconsistent, i.e. having ordinary solutions, weak solutions or notsolutions respectively. In this paper, the third type is divided in two classes: strict-strongly and quasi-strongly inconsistent and is given a topology over a quotient space of the set of systems over finite- dimensional spaces, that yields a set of...
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