Geodesic
Spectral problems of dissipative singular q-Sturm–Liouville operators in limit-circle case
Filomat, Tome 36 (2022) no. 9, p. 2891

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DOI

We consider the dissipative singular q-Sturm–Liouville operators acting in the Hilbert space L 2 w,q (R +), that the extensions of a minimal symmetric operator with deficiency indices (2, 2) (in limit-circle case). We construct a self-adjoint dilation of the dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation in terms of the Weyl–Titchmarsh function of a self-adjoint q-Sturm-Liouville operator. We also construct a functional model of the dissipative operator and determine its characteristic function in terms of the scattering matrix of the dilation (or of the Weyl–Titchmarsh function). Theorems on the completeness of the system of or root functions of the dissipative and accumulative q-Sturm–Liouville operators are proved.
DOI : 10.2298/FIL2209891A
Classification : 39A13, 33D05, 34B05, 34B24, 47A20, 47B25, 47B44, 47A40
Keywords: q-Sturm-Liouville equation, limit-circle, dissipative operator, self-adjoint dilation, scattering matrix, characteristic function, completeness of the root functions 
Bilender P Allahverdiev. Spectral problems of dissipative singular q-Sturm–Liouville operators in limit-circle case. Filomat, Tome 36 (2022) no. 9, p. 2891 . doi: 10.2298/FIL2209891A
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     author = {Bilender P Allahverdiev},
     title = {Spectral problems of dissipative singular {q-Sturm{\textendash}Liouville} operators in limit-circle case},
     journal = {Filomat},
     pages = {2891 },
     year = {2022},
     volume = {36},
     number = {9},
     doi = {10.2298/FIL2209891A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2209891A/}
}
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