Article
Ufa Mathematical Journal
Volume 8, Number 4, pp. 123-130
Perturbation of a surjective convolution operator
Musin I.Kh.
DOI:10.13108/2016-8-4-123
Download PDF
Article on MathNetAbstact
Let $\mu \in {\mathcal E}'({\mathbb R}^n)$ be a compactly supported distribution such that its support is a convex set with a non-empty interior.
Let $X_2$ be a convex domain in ${\mathbb R}^n$, $X_1 = X_2 + \mathrm{supp}\,\mu $. Let the convolution operator $A: {\mathcal E}(X_1) \to {\mathcal E}(X_2)$ acting by the rule $(Af)(x) = (\mu * f)(x)$ is surjective. We obtain a sufficient condition for a linear continuous operator $B: {\mathcal E}(X_1) \to {\mathcal E}(X_2)$ ensuring the surjectivity of the operator $A+B$.