This paper is an extended version of an invited talk presented during the Orlicz Centenary Conference (Poznań, 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 Proj¹ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc64-0-5,
author = {Pawe\l\ Doma\'nski},
title = {Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives},
journal = {Banach Center Publications},
volume = {65},
year = {2004},
pages = {51-70},
zbl = {1061.46003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc64-0-5}
}
Paweł Domański. Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives. Banach Center Publications, Tome 65 (2004) pp. 51-70. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc64-0-5/