International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 9, Pages 557-574

On the spectra of non-selfadjoint differential operators and their adjoints in direct sum spaces

Sobhy El-Sayed Ibrahim

Department of Mathematics, Faculty of Science, Benha University, Kalubia, Benha 13518, Egypt

Received 20 May 2001

Copyright © 2003 Sobhy El-Sayed Ibrahim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The general ordinary quasidifferential expression Mp of nth order, with complex coefficients and its formal adjoint Mp+ on any finite number of intervals Ip=(ap,bp), p=1,, N, are considered in the setting of the direct sums of Lwp2(ap,bp)-spaces of functions defined on each of the separate intervals. And a number of results concerning the location of the point spectra and regularity fields of general differential operators generated by such expressions are obtained.