Separability of the third-order differential operator given on the whole plane

Abstract

In this paper, in the space L_2(R^2), we study a third-order differential operator with continuous coefficients in R(−∞, +∞). Here, these coefficients can be unlimited functions at infinity. In addition under some restrictions on the coefficients, the bounded invertibility of the given operator is proved and a coercive estimate is obtained, i.e. separability is proved.