On the domains of regularly solvable operators in the direct sum spaces

Abstract

A general ordinary quasi-differential expressions τ_(1 ),τ_(2 ),…,τ_(n ) each of order n with complex coefficients and their formal adjoint are τ_1^+, τ_2^+, …, τ_n^+ can be defined on the interval [a, b) respectively, we give a characterization of all regularly solvable operators and their adjoints generated by a general ordinary quasi-differential expressions τ_(jp )in the direct sum of Hilbert spaces L_(w )^2 (a_p,b_p ),p=1,…,N. This characterization is an extension of those obtained in the case of one interval with one and two singular end-points, and is a generalization of those proved in the symmetric case.