当前位置: X-MOL 学术Russ. Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Inhomogeneous Hilbert Boundary Value Problem with Several Points of Logarithmic Turbulence
Russian Mathematics Pub Date : 2021-02-15 , DOI: 10.3103/s1066369x21010059
P. L. Shabalin , A. Kh. Fatykhov

In the unit disk, we consider the Hilbert boundary value problem. Its coefficient is assumed to be Hölder continuous everywhere on the unit circle excluding a finite set of points. At these points, the argument of the coefficient has non-removable discontinuity of logarithmic order. We obtain formulas for the general solution and fully describe the solvability of the problem in the class of functions, analytic and bounded in the unit disc. Our technique is based on the theory of entire functions of zero proximate order and the geometric theory of functions of a complex variable. We apply the obtained results to the study of the solvability of a boundary value problem for generalized analytic function.



中文翻译:

具有对数湍流多点的非均匀希尔伯特边值问题

在单位磁盘中,我们考虑希尔伯特边值问题。假定其系数在单位圆上的任意位置都是Hölder连续的,不包括一组有限的点。在这些点上,系数的自变量具有对数阶的不可移动不连续性。我们获得了一般解的公式,并在单位圆盘中的函数类,解析和有界的范围内充分描述了问题的可解性。我们的技术基于零次阶完整函数的理论和复变量函数的几何理论。我们将获得的结果应用于广义解析函数的边值问题的可解性研究。

更新日期:2021-02-16
down
wechat
bug