The Regularly Solvable Operators with Their Products and Spectra in Direct Sum Spaces


The generic quasi-differential expressions _1,_2,…, n of order n with complex coefficients and their formal adjoints on the interval are studied in this study (a,b). It is illustrated in direct sum spaces L w2 (I (p)),p=1,2,…,N of functions defined on each of the independent intervals with one and two unique end-points, and when all solutions of the product equation [_(j=1)n j -w]u=0 and its adjoint [_(j=1)n j+ – w]v=0 Because all well-posed extensions of the minimum operator T 0 (_1,_2,…, n) have resolvents that are Hilbert-Schmidt integral operators and so have a totally discrete spectrum in L w2 (a,b) (the limit circle case). This means that all the usual essential spectra for all the regularly solvable operators are empty. These findings build on those of formally published research expressive symmetric and generic quasi-differential expressions

Author(S) Details

Sobhy El-sayed Ibrahim
Department of Mathematics, Faculty of Science, Benha University, P.O.Box 13518, Benha, Egypt

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