International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 11, Pages 695-709

On the domain of selfadjoint extension of the product of Sturm-Liouville differential operators

Sobhy El-Sayed Ibrahim

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

Received 10 August 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 second-order symmetric Sturm-Liouville differential expressions τ1,τ2,,τn with real coefficients are considered on the interval I=(a,b), a<b. It is shown that the characterization of singular selfadjoint boundary conditions involves the sesquilinear form associated with the product of Sturm-Liouville differential expressions and elements of the maximal domain of the product operators, and it is an exact parallel of the regular case. This characterization is an extension of those obtained by Everitt and Zettl (1977), Hinton, Krall, and Shaw (1987), Ibrahim (1999), Krall and Zettl (1988), Lee (1975/1976), and Naimark (1968).