On the Product of Self-Adjoint Sturm-Liouville Differential Operators in Direct Sum Spaces

Sobhy El-Sayed Ibrahim

Abstract


In this paper, the second-order symmetric Sturm-Liouville differential expressions $\tau _1,\tau _2,\ldots,\tau _n$ with real coefficients on any finite number of intervals are studied in the setting of the direct sum of the $L_w^2$-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].

Keywords


Sturm-Liouville differential expressions; Product differential expressions; Deficiency indices; Regular and singular end-points; Integrable square solutions; Direct sum spaces; Boundary conditions

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DOI: http://dx.doi.org/10.26713%2Fjims.v4i1.71

eISSN 0975-5748; pISSN 0974-875X