# A splitting theory for the space of distributions

Studia Mathematica (2000)

- Volume: 140, Issue: 1, page 57-77
- ISSN: 0039-3223

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topDomański, P., and Vogt, D.. "A splitting theory for the space of distributions." Studia Mathematica 140.1 (2000): 57-77. <http://eudml.org/doc/216756>.

@article{Domański2000,

abstract = {The splitting problem is studied for short exact sequences consisting of countable projective limits of DFN-spaces (*) 0 → F → X → G → 0, where F or G are isomorphic to the space of distributions D'. It is proved that every sequence (*) splits for F ≃ D' iff G is a subspace of D' and that, for ultrabornological F, every sequence (*) splits for G ≃ D' iff F is a quotient of D'},

author = {Domański, P., Vogt, D.},

journal = {Studia Mathematica},

keywords = {exact complex; systems of partial differential equations; short exact sequence; splitting; space of distributions; lifting of Banach discs; Schwartz spaces; nuclear spaces; ultrabornological associated space; ω; complete splitting theory; short exact sequences; countable projective limits of DFN-spaces; PLS-spaces; PLN-spaces; ultrabornological},

language = {eng},

number = {1},

pages = {57-77},

title = {A splitting theory for the space of distributions},

url = {http://eudml.org/doc/216756},

volume = {140},

year = {2000},

}

TY - JOUR

AU - Domański, P.

AU - Vogt, D.

TI - A splitting theory for the space of distributions

JO - Studia Mathematica

PY - 2000

VL - 140

IS - 1

SP - 57

EP - 77

AB - The splitting problem is studied for short exact sequences consisting of countable projective limits of DFN-spaces (*) 0 → F → X → G → 0, where F or G are isomorphic to the space of distributions D'. It is proved that every sequence (*) splits for F ≃ D' iff G is a subspace of D' and that, for ultrabornological F, every sequence (*) splits for G ≃ D' iff F is a quotient of D'

LA - eng

KW - exact complex; systems of partial differential equations; short exact sequence; splitting; space of distributions; lifting of Banach discs; Schwartz spaces; nuclear spaces; ultrabornological associated space; ω; complete splitting theory; short exact sequences; countable projective limits of DFN-spaces; PLS-spaces; PLN-spaces; ultrabornological

UR - http://eudml.org/doc/216756

ER -

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