The algebra of all Dirichlet series that are uniformly convergent in the half-plane of complex numbers with positive real part is investigated. When it is endowed with its natural locally convex topology, it is a non-nuclear Fréchet Schwartz space with basis. Moreover, it is a locally multiplicative algebra but not aQ-algebra. Composition operators on this space are also studied.

This is an expository paper where we relate some aspects of the problem of looking for holomorphic functions with maximal cluster sets under the action of operators defined on spaces of holomorphic functions. Some functional generalizations of cluster sets, as well as special spaces of analytic functions, are also considered.

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In this paper an exact series solution for homogeneous parabolic coupled systems is constructed using a projection method. An illustrative example is given.