The Products of Regularly Solvable Operators with Their Spectra in Direct Sum Spaces
- 1 Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
Abstract
In this paper, we consider the general quasi-differential expressions each of order n with complex coefficients and their formal adjoints on the int erval ( a , b ). It is shown in direct sum spaces of functions defined on each of the separate intervals with the cases of one and two singular end-points and when all solutions of the equation and its adjoint are in (the limit circle case) that all well-posed extensions of the minimal operator have resolvents which are HilbertSchmidt integral operators and consequently have a wholly discrete spectrum. This implies that all the regularly solvable operators have all the standard essential spectra to be empty. These results extend those of formally symmetric expression studied in [1-10] and those of general quasi-differential expressions in [11-19].
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