On a Spectral Problem for the Cauchy–Riemann Operator with Boundary Conditions of the Bitsadze–Samarskii Type
Imanbaev N.S.
March 2023Pleiades Publishing
Lobachevskii Journal of Mathematics
2023#44Issue 31162 - 1170 pp.
Abstract: In the functional space C(|z| ≤ 1) is considered a spectralproblem for the Cauchy–Riemann operator with boundary conditionsof the Bitsadze–Samarskii type. It is proved under the assumptionthat when 0 ∈ ρ(K) is a non-empty resolvent set of theoperator K , the considered spectral problem for theCauchy–Riemann operator is reduced to a singular integralequation with a continuous kernel.
Bitsadze–Samarskii type boundary conditions , Cauchy–Riemann operator , continuous kernel , regular boundary conditions , resolvent set , singular integral equation
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South Kazakhstan State Pedagogical University, Shymkent, 160000, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
South Kazakhstan State Pedagogical University
Institute of Mathematics and Mathematical Modeling
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