Holomorphic Degenerate Groups of Operators in Quasi-Banach Spaces

Abstract

Probably, Sobolev type equations, i.e. unsolved with respect to the highest derivative, first appeared in the late nineteenth century. Due to the fact that the interest to the Sobolev type equations recently significantly increased, the need arose for their consideration in quasi-Banach spaces. Specifically, this study aimed at understanding non-classical models of mathematical physics in quasi-Banach spaces.

The theory of holomorphic degenerate groups of operators, developed in Banach spaces and Frechet spaces is transferred to quasi-Banach spaces. Abstract results are illustrated by specific examples.

The article besides the introduction and the references contains three parts. The first part provides the necessary information regarding the theory of relatively p-bounded operators in quasi-Banach spaces. The second one represents the construction of the holomorphic group of solving operators. The third part contains the sufficient conditions for pair of operators to generate group of solving operators