Geodesic
Perturbation of a~surjective convolution operator
Ufa mathematical journal, Tome 8 (2016) no. 4, pp. 123-130

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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 $A\colon\mathcal E(X_1)\to\mathcal E(X_2)$ acting by the rule $(Af)(x)=(\mu*f)(x)$ is surjective. We obtain a sufficient condition for a linear continuous operator $B\colon\mathcal E(X_1)\to\mathcal E(X_2)$ ensuring the surjectivity of the operator $A+B$.
Keywords: convolution operator, entire functions.
Mots-clés : distribution, Fourier–Laplace transform 
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     author = {I. Kh. Musin},
     title = {Perturbation of a~surjective convolution operator},
     journal = {Ufa mathematical journal},
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     publisher = {mathdoc},
     volume = {8},
     number = {4},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2016_8_4_a8/}
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I. Kh. Musin. Perturbation of a~surjective convolution operator. Ufa mathematical journal, Tome 8 (2016) no. 4, pp. 123-130. http://geodesic.mathdoc.fr/item/UFA_2016_8_4_a8/