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Hadamard operators on D ′ ( Ω )
Author(s) -
Vogt Dietmar
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600305
Subject(s) - mathematics , hadamard transform , monomial , convolution (computer science) , hadamard three lines theorem , linear operators , multiplicative function , eigenvalues and eigenvectors , pure mathematics , operator theory , algebra over a field , mathematical analysis , hadamard matrix , computer science , physics , quantum mechanics , machine learning , artificial neural network , bounded function
For open sets Ω ⊂ R dwe study Hadamard operators on D′ ( Ω ) , that is, continuous linear operators which admit all monomials as eigenvectors. We characterize them as operators of the form L ( S ) = S ★ T where T is a distribution and ⋆ the multiplicative convolution. This extends previous results for the case of Ω = R dbut requires essentially different methods.