Abstract
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(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 multipoint Vallée Poussin problem.
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Original Russian Text © V.V. Napalkov, A.U.Mullabaeva, 2014, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Vol. 20, No. 1.
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Napalkov, V.V., Mullabaeva, A.U. On one class of differential operators and their application. Proc. Steklov Inst. Math. 288 (Suppl 1), 142–155 (2015). https://doi.org/10.1134/S0081543815020145
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DOI: https://doi.org/10.1134/S0081543815020145