PRINCIPAL FUNCTIONS OF NON-SELFADJOINT MATRIX STURM ñ LIOUVILLE OPERATORS WITH BOUNDARY CONDITIONS DEPENDENT ON THE SPECTRAL PARAMETER

Abstract

bstract. Let L denote operator generated in L2(R+; E) by the di§erential expression l(y) = y 00 + Q(x)y; x 2 R+ := [0; 1) ; and the boundary condition Y 0 (0; )( 0 + 1 + 2 2 )Y (0; ) = 0 , where Q is a non-selfadjoint matrix-valued function and 0 ; 1 ; 2 are non-selfadjoint matrices, also 2 is invertible: In this paper, we investigate the principal functions correspending to the eigenvalues and the spectral singularities of L.