EQUIVALENT ALGEBRAS OF SINGULAR INTEGRAL OPERATORS. NOETHERIAN CRITERIONS

Diana BÂCLEA, Vasile NEAGU* Universitatea de Stat din Cahul *Universitatea de Stat din Moldova

Abstract

In the present work there are established necessary and sufficient conditions under which sungular integral operators with shift of Carleman tipe are Notherian, the symbol of these operators is determined and index of these operators is calculated. These results are obtained due to the study of the algebra, generated by these operators in the space Lp with a certain weight, chosen in such a way, that continuity of operators is ensured. In the study of this algebra an important role has the notion of equivalence of Banach algebras, introduced by mathematicians I. Gohberg and N.Krupnik. Keywords: singular integral operator, noetherian operator, symbol.