Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives

Volume 64 / 2004

Pawe/l Doma/nski Banach Center Publications 64 (2004), 51-70 MSC: Primary: 46A13, 46E10, 46F05, 35E20, 35N05. Secondary: 35A05, 45E10, 46A03, 46A11, 46M18, 26E10. DOI: 10.4064/bc64-0-5


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.


  • Pawe/l Doma/nskiFaculty of Mathematics and Computer Science
    A. Mickiewicz University Pozna/n
    Institute of Mathematics
    Polish Academy of Sciences, Pozna/n branch
    Umultowska 87, 61-614 Pozna/n, Poland

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