MR3667002 Reviewed Vogt, Dietmar(D-BUW) Hadamard operators on D′(Ω). (English summary) Math. Nachr. 290 (2017), no. 8-9, 1374–1380. 46F10 (46F12 47B38)

Risultato della ricerca: Other contribution

Abstract

In this paper, the Hadamard operators, i.e. a particular class of continuous linear operators on D′(Ω) whose set of eigenvectors is the class of monomials, are considered on an open set Ω⊂Rd. Specifically, Hadamard operators L are characterized by the multiplicative convolution, that is, there exists a distribution T such that L(S)=S⋆T, where the multiplicative convolution ⋆ is defined by (S⋆T)ϕ=Sy(Txϕ(xy)). To obtain this characterization, the author defines a particular extension to D(Ω˜), where Ω˜:=⋃a∈RdaΩ, of the transpose of Hadamard operators. This result is a generalization of a previous work of the author where only the case Ω=Rd was considered.
Lingua originaleEnglish
Numero di pagine1
Stato di pubblicazionePublished - 2017

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title = "MR3667002 Reviewed Vogt, Dietmar(D-BUW) Hadamard operators on D′(Ω). (English summary) Math. Nachr. 290 (2017), no. 8-9, 1374–1380. 46F10 (46F12 47B38)",
abstract = "In this paper, the Hadamard operators, i.e. a particular class of continuous linear operators on D′(Ω) whose set of eigenvectors is the class of monomials, are considered on an open set Ω⊂Rd. Specifically, Hadamard operators L are characterized by the multiplicative convolution, that is, there exists a distribution T such that L(S)=S⋆T, where the multiplicative convolution ⋆ is defined by (S⋆T)ϕ=Sy(Txϕ(xy)). To obtain this characterization, the author defines a particular extension to D(Ω˜), where Ω˜:=⋃a∈RdaΩ, of the transpose of Hadamard operators. This result is a generalization of a previous work of the author where only the case Ω=Rd was considered.",
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