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Abstract

This paper is an extended version of an invited talk presented during the Orlicz Centenary Conference (Pozna/n, 2003). It contains a brief survey of applications to classical problems of analysis of the theory of the so-called PLS-spaces (in particular, spaces of distributions and real analytic functions). Sequential representations of the spaces and the theory of the functor $\mathop{\rm Proj}^1$ are applied to questions like solvability of linear partial differential equations, existence of a solution depending linearly and continuously on the right hand side of the equation and existence of a solution depending analytically on parameters.