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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.
Paweł Domański. "Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives." Banach Center Publications 64.1 (2004): 51-70. <http://eudml.org/doc/281730>.
@article{PawełDomański2004, abstract = {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.}, author = {Paweł Domański}, journal = {Banach Center Publications}, keywords = {space of real analytic functions; space of distributions; ultradifferentiable functions; ultradistributions; linear partial differential operators; solvability; linear continuous right inverse; analytic dependence on parameters; Proj functor; sequential representation; PLS-spaces; locally convex spaces}, language = {eng}, number = {1}, pages = {51-70}, title = {Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives}, url = {http://eudml.org/doc/281730}, volume = {64}, year = {2004}, }
TY - JOUR AU - Paweł Domański TI - Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives JO - Banach Center Publications PY - 2004 VL - 64 IS - 1 SP - 51 EP - 70 AB - 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. LA - eng KW - space of real analytic functions; space of distributions; ultradifferentiable functions; ultradistributions; linear partial differential operators; solvability; linear continuous right inverse; analytic dependence on parameters; Proj functor; sequential representation; PLS-spaces; locally convex spaces UR - http://eudml.org/doc/281730 ER -