A Hilbert Boundary Value Problem for Generalised Cauchy-Riemann Equations

被引：0

作者：

Alsaedy, Ammar ^{[1
,2
]}

Tarkhanov, Nikolai ^{[2
]}

机构：

[1] Alnahrain Univ, Dept Math, Coll Sci, Baghdad, Iraq

[2] Univ Potsdam, Inst Math, Karl Liebknecht Str 24-25, D-14476 Golm, Germany

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2017年 / 27卷 / 02期

关键词：

Dirac operator; Clifford algebra; Riemann-Hilbert problem; Fredholm operators;

D O I：

10.1007/s00006-016-0676-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We elaborate a boundary Fourier method for studying an analogue of the Hilbert problem for analytic functions within the framework of generalised Cauchy-Riemann equations. The boundary value problem need not satisfy the Shapiro-Lopatinskij condition and so it fails to be Fredholm in Sobolev spaces. We show a solvability condition of the Hilbert problem, which looks like those for ill-posed problems, and construct an explicit formula for approximate solutions.

引用

页码：931 / 953

页数：23

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