On the properties of systems of root functions of a second-order discontinuous operator

Abstract

In [1], a second-order discontinuous operator was studied and constructive necessary and sufficient conditions were established for the Riesz basis property of the system of root functions of this operator. These works played an important role in the study of the absolute and uniform convergence of biorthogonal expansions of -functions in terms of the root functions of the Schrodinger operator with multipoint boundary conditions [2, 3]. For a second-order discontinuous operator, we establish a necessary and sufficient condition for the Riesz basis property of its systems of root functions and analyze the absolute and uniform convergence and the rate of uniform convergence of biorthogonal expansions of discontinuous functions in terms of root functions.