International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 9, Pages 557-574
doi:10.1155/S0161171203007841
On the spectra of non-selfadjoint differential operators and their adjoints in direct sum spaces
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.
Abstract
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.