Polynomial ultradistributions: differentiation and Laplace transformation

O. Łopuszański

Banach Center Publications (2010)

  • Volume: 88, Issue: 1, page 195-209
  • ISSN: 0137-6934

Abstract

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We consider the multiplicative algebra P(𝒢₊') of continuous scalar polynomials on the space 𝒢₊' of Roumieu ultradistributions on [0,∞) as well as its strong dual P'(𝒢₊'). The algebra P(𝒢₊') is densely embedded into P'(𝒢₊') and the operation of multiplication possesses a unique extension to P'(𝒢₊'), that is, P'(𝒢₊') is also an algebra. The operation of differentiation on these algebras is investigated. The polynomially extended Laplace transformation and its connections with the differentiation are also studied.

How to cite

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O. Łopuszański. "Polynomial ultradistributions: differentiation and Laplace transformation." Banach Center Publications 88.1 (2010): 195-209. <http://eudml.org/doc/282213>.

@article{O2010,
abstract = {We consider the multiplicative algebra P(𝒢₊') of continuous scalar polynomials on the space 𝒢₊' of Roumieu ultradistributions on [0,∞) as well as its strong dual P'(𝒢₊'). The algebra P(𝒢₊') is densely embedded into P'(𝒢₊') and the operation of multiplication possesses a unique extension to P'(𝒢₊'), that is, P'(𝒢₊') is also an algebra. The operation of differentiation on these algebras is investigated. The polynomially extended Laplace transformation and its connections with the differentiation are also studied.},
author = {O. Łopuszański},
journal = {Banach Center Publications},
keywords = {ultradistributions on infinite-dimensional spaces; Laplace transform in ultradistribution spaces; spaces of polynomials},
language = {eng},
number = {1},
pages = {195-209},
title = {Polynomial ultradistributions: differentiation and Laplace transformation},
url = {http://eudml.org/doc/282213},
volume = {88},
year = {2010},
}

TY - JOUR
AU - O. Łopuszański
TI - Polynomial ultradistributions: differentiation and Laplace transformation
JO - Banach Center Publications
PY - 2010
VL - 88
IS - 1
SP - 195
EP - 209
AB - We consider the multiplicative algebra P(𝒢₊') of continuous scalar polynomials on the space 𝒢₊' of Roumieu ultradistributions on [0,∞) as well as its strong dual P'(𝒢₊'). The algebra P(𝒢₊') is densely embedded into P'(𝒢₊') and the operation of multiplication possesses a unique extension to P'(𝒢₊'), that is, P'(𝒢₊') is also an algebra. The operation of differentiation on these algebras is investigated. The polynomially extended Laplace transformation and its connections with the differentiation are also studied.
LA - eng
KW - ultradistributions on infinite-dimensional spaces; Laplace transform in ultradistribution spaces; spaces of polynomials
UR - http://eudml.org/doc/282213
ER -

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