Hadamard operators on D'(Ω)

الأصل · EN

For open sets Ω⊂ Rᵈ we 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=Rᵈ but requires essentially different methods.