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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...
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...
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