Abstract
The theory of holomorphic degenerate semigroups of operators was constructed earlier in Banach spaces and Frechet spaces. However, examples of study of mathematical objects show the necessity of their consideration in more general cases. In this article the theory of holomorphic degenerate semigroups of operators is transferred to quasi-Sobolev spaces of sequences which are quasi-normed and even quasi-Banach spaces. The article besides the introduction and references contains two paragraphs. In the first, resolving analytic degenerate semigroups are constructed. The second paragraph includes the study of kernels and images of analytic semigroups.
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