Geodesic
The Riemann problem in a half-plane for generalized analytic functions with a singular line
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2023), pp. 78-89

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In this paper we have studied an inhomogeneous boundary value problem Riemann with a finite index and a boundary condition on the real axis for one generalized Cauchy-Riemann equation with singular coefficients. To solve this problem, we derived a structural formula for the general solution of the generalized equation and conducted a complete study of the solvability of the Riemann boundary value problem of the theory of analytic functions with an infinite index of logarithmic order. Based on the results of this study, we derived a formula for a general solution and studied the existence and number of solutions boundary value problems for generalized analytical functions.
Keywords: Riemann problem, generalized analytic function, infinite index, entire function of given order zero. 
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     author = {P. L. Shabalin and R. R. Faizov},
     title = {The {Riemann} problem in a half-plane for generalized analytic functions with a singular line},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {78--89},
     publisher = {mathdoc},
     number = {3},
     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/IVM_2023_3_a6/}
}
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P. L. Shabalin; R. R. Faizov. The Riemann problem in a half-plane for generalized analytic functions with a singular line. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2023), pp. 78-89. http://geodesic.mathdoc.fr/item/IVM_2023_3_a6/