A splitting theory for the space of distributions

P. Domański; D. Vogt

Studia Mathematica (2000)

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

Abstract

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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'

How to cite

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Domański, 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 -

References

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