Homogeneous Hilbert boundary-value problem with several points of turbulence

被引：2

作者：

Fatykhov A.K. ^{[1
]}

Salimov R.B. ^{[1
]}

Shabalin P.L. ^{[1
]}

机构：

[1] Kazan State University of Architecture and Engineering, ul. Zelenaya 1, Kazan

来源：

Lobachevskii Journal of Mathematics | 2017年 / 38卷 / 3期

关键词：

entire functions; growth indicator; infinite index; maximum principle; Riemann–Hilbert problem;

D O I：

10.1134/S199508021703009X

中图分类号：

学科分类号：

摘要：

We consider Riemann–Hilbert boundary value problem with infinite index in unit disk. Its coefficient is Hölder-continuous everywhere on the unit circle excluding a finite set of points, where its argument has power discontinuities of order less one. The present article is the first research of this version of Hilbert boundary-value problem with infinite index. We obtain formulas for its general solution, investigate existence ad uniqueness of solutions, and describe the set of solutions in the case of non-uniqueness. Our technique is based on theory of entire functions and geometric theory of functions. © 2017, Pleiades Publishing, Ltd.

引用

页码：414 / 419

页数：5

共 8 条

[1]

Govorov N.V., The Riemann Boundary Value Problemwith an Infinite Index, (1986)

[2]

Tolochko M.E., About the solvability of the homogeneous Riemann boundary value problem for the half-plane with infinite index, Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauki, 4, pp. 52-59, (1969)

[3]

Sandrygaylo I.E., On Riemann–Hilbert boundary value problem for the half-plane with infinite index, Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauki, 6, pp. 16-23, (1974)

[4]

Monahov V.N., Semenko E.V., Boundary value problem with infinite index inHardy spaces, Akad.Nauk SSSR, 291, pp. 544-547, (1986)

[5]

Salimov R.B., Shabalin P.L., Hilbert boundary value problem of the theory analytic functions and its applications, (2005)

[6]

Hurwitz A., Courant R., Vorlesungen über Allgemeine Funktionentheorie und Elliptische Funktionen, (1925)

[7]

Salimov R.B., Shabalin P.L., On solvability of homogeneous Riemann–Hilbert problem with countable set of coefficient discontinyities and two-side curlingat infinity of order less than 1/2, Ufa Mat. Zh., 5, 2, pp. 82-93, (2013)

[8]

Levin B.Y., Distribution of Zeros of Entire Functions, (1956)

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