On the Essential Spectra of Regularly Solvable Operators in the Direct Sum Spaces

The problem of investigation of the spectral properties of the operators which are regularly solvable with respect to minimal operators T 0 (M p ) and T 0 (M + p ) generated by a general quasi-differential expression M p and its formal adjoint M + p on any finite number of intervals I p = (a p , b p ), p = 1, . . . , N, are studied in the setting of the direct sums of L 2 wp (a p , b p )-spaces of functions defined on each of the separate intervals. These results extend those of formally symmetric expression M studied in [1] and [15] in the single-interval case, and also extend those proved in [10] and [13] in the general case.

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