A Hilbert Boundary Value Problem for Generalised Cauchy–Riemann Equations

被引：0
|
作者：
Ammar Alsaedy
Nikolai Tarkhanov
机构：
[1] Alnahrain University,Department of Mathematics, College of Science
[2] University of Potsdam,Institute of Mathematics
来源：
Advances in Applied Clifford Algebras | 2017年 / 27卷
关键词：
Dirac operator; Clifford algebra; Riemann–Hilbert problem; Fredholm operators; Primary 35F45; Secondary 35J56; 47N20;
D O I：
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中图分类号：
学科分类号：
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.
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页码：931 / 953
页数：22
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