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Krein’s Theorems for a Dissipative Boundary Value Transmission Problem

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Abstract

Let us consider the differential expression

$$\ell (y)=-y^{\prime \prime }+q(x)y,\quad x\in I:=[0,c)\cup (c,\infty ),$$

where c is a transmission point and is regular for the differential expression (y). We assume that Weyl’s limit-circle case holds for the differential expression (y) on I. In this paper, using Krein’s theorems, we investigate the completeness of the root vectors of a singular dissipative boundary value transmission problem generated by (y).

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Correspondence to Elgiz Bairamov.

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Communicated by Aad Dijksma.

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Bairamov, E., Ugurlu, E. Krein’s Theorems for a Dissipative Boundary Value Transmission Problem. Complex Anal. Oper. Theory 7, 831–842 (2013). https://doi.org/10.1007/s11785-011-0180-z

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  • DOI: https://doi.org/10.1007/s11785-011-0180-z

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