Özet:

The main objective of this study is to study some spectral characteristics of differential operators from the second staircase produced by the two interim uninterrupted limit-value-transition problem with transitional conditions at a non-continuity point. An operator-theoretical method for the study of the behaviors of the spectrum and the characteristics of the self-functions system has been introduced. For this first we have identified new spaces, which are characteristic of our very interim border-value-passion problem, and internal interfaces that are characteristic of these spaces. The conditional boundary-value-passing problem of the jump we’ve studied is reduced to the integral equation in the direct total space of the Sobolev spaces, and this problem is defined as a generalized solution concept. Considering that the two-intermediate uninterrupted limit-value-passing problem can be reduced to an operator-demet equation with the help of the Riesz representation theory, some self-compatible and compact operators have been identified in the appropriate Sobolev spaces. It was later proven that this operator-polinom was positively defined.

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