Hilbert Problem for the Cauchy–Riemann Equation with a Singular Circle and a Singular Point

Rasulov, A. B.; Bobodzhanova, M. A.; Fedorov, Yu. S.

doi:10.1007/s10958-019-04427-2

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“…a refined zero-order ρ(|ζ|) ≤ ln ln 2 |ζ |/ln|ζ | with a restriction on the growth of its boundary values in the form of inequalities (25). For a function…”

Section: Theoremmentioning

confidence: 99%

“…Rasulov, A.P. Soldatov, U.S. Fedorov, Bobodzhanova M.A., and others (for example, [24][25][26][27]). In these papers, the method for solving the boundary value problem for equation ( 1) is based on a reduction to a similar problem for analytic functions.In this case (for example, [28,29]), it is possible to formulate boundary value problems for generalized analytic functions with a singular line, when the coefficients of equation (1) delegate their features to the boundary condition of the problem for analytic functions and turn the latter into a problem with an infinite index.…”

Section: Introductionmentioning

confidence: 99%

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Hilbert boundary value problem for generalized analytic functions with a singular line

Шабалин¹,

Faizov²

2021

E3S Web Conf.

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In this paper, we study an inhomogeneous Hilbert boundary value problem with a finite index and a boundary condition on a circle for a generalized Cauchy-Riemann equation with a singular coefficient. To solve this problem, we conducted a complete study of the solvability of the Hilbert boundary value problem of the theory of analytic functions with an infinite index due to a finite number of points of a special type of vorticity. Based on these results, we have derived a formula for the general solution and studied the existence and number of solutions to the boundary value problem of the theory of generalized analytic functions.

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“…a refined zero-order ρ(|ζ|) ≤ ln ln 2 |ζ |/ln|ζ | with a restriction on the growth of its boundary values in the form of inequalities (25). For a function…”

Section: Theoremmentioning

confidence: 99%