International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 11, Pages 695-709
doi:10.1155/S0161171203008020
On the domain of selfadjoint extension of the product of Sturm-Liouville differential operators
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.
Abstract
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).