On the product of self-adjoint Sturm-Liouville differential operators in direct sum spaces

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Sobhy El-Sayed Ibrahim

Abstract

In this paper, the second-order symmetric Sturm-Liouville differential expressions τ1,τ2,,τn, with real coefficients on any finite number of intervals are studied in the setting of the direct sum of the L2w-spaces of functions defined on each of the separate intervals. It is shown that the characterization of singular self-adjoint 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, it is an exact parallel of that in the regular case. This characterization is an extension of those obtained in [6], [7], [8], [9], [12], [14] and [15].

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How to Cite
Ibrahim, S. E.-S. (2006). On the product of self-adjoint Sturm-Liouville differential operators in direct sum spaces. Tamkang Journal of Mathematics, 37(1), 77–92. https://doi.org/10.5556/j.tkjm.37.2006.181
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Papers
Author Biography

Sobhy El-Sayed Ibrahim

Department of Mathematics, Faculty of Science, Benha University, P.O.Box 13518 Benha, Egypt.