Invariant linear functionals on L(R+)

研究成果: Article

抄録

We consider a continuous version of the classical notion of Banach limits, i.e., normalized positive linear functionals on L(R+) invariant under translations f(x)↦f(x+s) of L(R+) for every s≥0. We give one of its characterizations in terms of the invariance under the operation of a certain linear transformation on L(R+). We also deal with invariant linear functionals under dilations f(x)↦f(rx), r≥1 and give a similar characterization via the Hardy operator. Applications to summability methods are presented in the last section.

元の言語English
記事番号123452
ジャーナルJournal of Mathematical Analysis and Applications
481
発行部数1
DOI
出版物ステータスPublished - 2020 1 1

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Linear Functionals
Banach Limit
Hardy Operator
Linear transformations
Invariant
Summability
Linear transformation
Invariance
Dilation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

これを引用

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AB - We consider a continuous version of the classical notion of Banach limits, i.e., normalized positive linear functionals on L∞(R+) invariant under translations f(x)↦f(x+s) of L∞(R+) for every s≥0. We give one of its characterizations in terms of the invariance under the operation of a certain linear transformation on L∞(R+). We also deal with invariant linear functionals under dilations f(x)↦f(rx), r≥1 and give a similar characterization via the Hardy operator. Applications to summability methods are presented in the last section.

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KW - Hardy operator

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