ON PROPER EXPANSIONS AND PROPER CONTRACTIONS OF NONLINEAR OPERATORS REPRESENTED IN THE FORM OF A PRODUCT
DOI:
https://doi.org/10.26577/JMMCS202512731Keywords:
Operator, correct expansion, correct contraction, regular expansion, Bitsadze-Samarskii type problemAbstract
Today there are many works devoted to the questions of expansion and contraction of operators [1–12]. In all these works the questions of expansion of the additive “minimal” operator and the questions of contraction of the additive “maximal” operator are considered. In this paper it is shown that these restrictions on the additivity of the corresponding operators are not essential. In [10] the questions of proper contraction of a maximal operator represented as a product are considered, i.e., the relationship between the set of proper contractions of the operator A = LM and the sets of proper contractions of the operators L and M is established. Here, an abstract theorem is proved which allows us to establish the relationship between the set of proper extensions of the operator A0 = L0M0 and the sets of proper extensions of the operators L0 and M0. In this connection, we prove an abstract theorem that allows us to describe the correct contractions of one class of nonlinear operators represented as a product.
