About one-parametrical semi-groups of transformations in weight anisotropic spaces of functions with integrated metrics (Q2833845)

The article is devoted to the proof of the theorem that the one-parameter family of linear transforms under consideration is a strongly continuous contractive semigroup in anisotropic spaces with an integral metric in \(\mathbb R^n\). The theorem gives the form of the generating operator of the indicated transformations. In the first part of this article, the authors give a proof of the theorem in \(\mathbb R^1\), and in the second part, the assertion of the theorem is proved in \(\mathbb R^n\).