Salimov, R. B.
Published in
Russian Mathematics

We study behavior of singular integral at neighborhood of the point at infinity. Its density satisfies the Hölder condition on the any finite part of the real axis, and at the infinity point it vanishes as power of logarithm with exponent lesser than −1.

Kats, B. A.
Published in
Russian Mathematics

The notice is dealing with contour integrals over non-smooth paths and their applications for solving of boundary-value problems. There is established that solvability of the Riemann boundary-value problem on non-smooth arc essentially depends on the type of its non-smoothness: on a zigzag-like arc we obtain the same picture of solvability as on sm...

Kuznetsov, S. P. Mochalov, V. V. Chuev, V. P.
Published in
Russian Mathematics

We pose and investigate the Riemann boundary-value problem for regular and strongly regular functions in Clifford algebras. The posed problem is reduced to the matrix problem for analytical functions in one and two complex variables and we give its solution. We carry out the boundary-value problems in special cases.

Salimov, R. B. Suleimanov, A. Z.
Published in
Russian Mathematics

We consider a Riemann boundary-value problem with infinite Gakhov’s index. The boundary data are defined on positive ray of the real axis. We solve the problem by means of removal of singularity of boundary data at the infinity. This approach is analogous to Gakhov’s method of elimination of singularities in the problemswith finite indices, but we ...

Kats, B. A.
Published in
Russian Mathematics

We study the Riemann boundary-value problem on non-rectifiable curves for holomorphic matrices with Fokas–Its–Kitaev asymptotics by means of the Cauchy transforms of certain distributions with supports on that curves. The main results concern the existence of solutions of sufficiently large degree.

Vafina, L. I. Salekhova, I. G.
Published in
Russian Mathematics

We solve the Schwarz problem for boundary contours consisting of countable sets of segments with limit point at infinity, including the periodic case. The solution is a result of a reduction to corresponding Riemann boundary-value problems.

Kats, D. B.
Published in
Russian Mathematics

We introduce certain new characteristics for non-rectifiable curves which allow to sharpen known solvability conditions for so-called jump boundary-value problems on that curves.

Kats, B. A. Kats, D. B.
Published in
Russian Mathematics

Let Γ be a simple Jordan arc in the complex plane. The Szegö function, by definition, is a holomorphic in ℂ \ Γ function with a prescribed product of its boundary values on Γ. The problem of finding the Segö function in the case of piecewise smooth Γ was solved earlier. In this paper we study this problem for non-rectifiable arcs. The solution reli...

Andriyanov, G. I.
Published in
Mathematical Notes

A new method of establishing the completeness of systems of analytic functions in the space A(D) is considered. We indicate some applications of the results obtained to the case of the principle of doubly symmetric Kaz’min sets, to the Abel-Goncharov problem (the uniqueness and construction problem), and to some other cases.

Bikchantaev, I. A.
Published in
Mathematical Notes

LetR be the Riemann surface of the functionu(z) specified by the equationun=P(z) withn ε ℕ,n ≥ 2, andz ε ℂ, whereP(z) is an entire function with infinitely many simple zeros. OnR, the Riemann boundary-value problem for an arbitrary piecewise smooth contour Γ is considered. Necessary and sufficient conditions for its solvability are obtained, and it...