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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.
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 -