A bisingular equation with translation in the space Lp

In this paper we use a local method to introduce and study the Noetherian nature of bisingular operators with translation in the space L_p. As corollaries to our general results we obtain criteria for the problem of linear conjugation with translation for analytic functions of two complex variables to be Noetherian.Translated from Matematicheskie Zametki, Vol. 13, No. 3, pp. 385–393, March, 1973.In conclusion, the author expresses his appreciation to V. A. Kakichev and V. S. Pilidi for their constant attention to this work.