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The dual space of precompact groups

M. Ferrer; S. Hernández; V. Uspenskij — 2013

Commentationes Mathematicae Universitatis Carolinae

For any topological group $G$ the dual object $\hat{G}$ is defined as the set of equivalence classes of irreducible unitary representations of $G$ equipped with the Fell topology. If $G$ is compact, $\hat{G}$ is discrete. In an earlier paper we proved that $\hat{G}$ is discrete for every metrizable precompact group, i.e. a dense subgroup of a compact metrizable group. We generalize this result to the case when $G$ is an almost metrizable precompact group.

A matrix constructive method for the analytic-numerical solution of coupled partial differential systems

Lucas Jódar; Enrique A. Navarro; M. V. Ferrer — 1995

Applications of Mathematics

In this paper we construct analytic-numerical solutions for initial-boundary value systems related to the equation $u_{t} - A u_{x x} - B u = 0$ , where $B$ is an arbitrary square complex matrix and $A$ ia s matrix such that the real part of the eigenvalues of the matrix $\frac{1}{2} (A + A^{H})$ is positive. Given an admissible error $ε$ and a finite domain $G$ , and analytic-numerical solution whose error is uniformly upper bounded by $ε$ in $G$ , is constructed.

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