Geodesic
Spectral properties of boundary-value problem with a~shift for wave equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2016), pp. 48-54

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We consider the differential operator given by the wave equation with potential in characteristic triangle and boundary conditions: with shift on the characteristics and oblique derivative on noncharacteristic boundary. We obtain condition for the Volterra property of problem. In remaining cases we show the completeness of the root functions. For cases when the potential depends on a single variable, we study questions of the basis (not basis) property for the system of root functions.
Keywords: wave equation, Riesz basis, regular boundary conditions, eigenvalues, root functions. 
@article{IVM_2016_3_a4,
     author = {N. A. Yessirkegenov and M. A. Sadybekov},
     title = {Spectral properties of boundary-value problem with a~shift for wave equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {48--54},
     publisher = {mathdoc},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_3_a4/}
}
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N. A. Yessirkegenov; M. A. Sadybekov. Spectral properties of boundary-value problem with a~shift for wave equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2016), pp. 48-54. http://geodesic.mathdoc.fr/item/IVM_2016_3_a4/