Geodesic
On one class of differential operators and their application
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 201-214

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We use a generalized differentiation operator to construct a generalized shift operator, which makes it possible to define a generalized convolution operator in the space $H(\mathbb C)$. Next, we consider the characteristic function of this operator and introduce a generalized Laplace transform. We study the homogeneous equation of the generalized convolution operator, investigate its solvability, and consider the multi-point Vallée Poussin problem.
Keywords: generalized Bargmann–Fock space, generalized differentiation operator, eigenfunction, generalized Laplace transform, characteristic function, generalized shift operator, generalized convolution operator, sequentially sufficient set, uniqueness set
Mots-clés : Vallée Poussin problem. 
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V. V. Napalkov; A. U. Mullabaeva. On one class of differential operators and their application. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 201-214. http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a18/