ASUPRA ECHIVALENȚEI UNOR ALGEBRE DE OPERATORI INTEGRALI CU TRANSLAȚII ÎN SPAȚIILE 푳 풑 CU PONDERI

Galina VORNICESCU Universitatea de Stat din Tiraspol

Abstract

ON THE EQUIVALENCE OF SOME ALGEBRAS OF INTEGRAL OPERATORS WITH SHIFT IN 푳 풑 SPACES WITH WEIGHTS This paper demonstrates that some integral operator algebras are equivalent to the algebra generated by singular integral operators with piecewise continuous coefficients. With the help of equivalence, the notion of symbol is defined for the operators in the algebras approached in this paper, it is established that the Noetherian conditions and the indices of the operators are expressed by determinant of their symbols. In the study of the respective algebras certain results of the mathematicians I.Gohberg and N.Krupnik are used. Keywords: singular integral operator, Noetherian operator, regularisation, symbol.