Two-interval Sturm–Liouville operators in modified Hilbert spaces

By modifying the inner product in the direct sum of the Hilbert spaces associated with each of two underlying intervals on which the Sturm–Liouville equation is defined, we generate self-adjoint realizations for boundary conditions with any real coupling matrix whose determinant is positive. This contrasts with the usual theory which requires the coupling matrix to have determinant one. © 2006 Elsevier Inc. All rights reserved