A Hilbert Boundary Value Problem for Generalised Cauchy-Riemann Equations
- 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.
| Author details: | Ammar AlsaedyORCiD, Nikolai Nikolaevich TarkhanovORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1007/s00006-016-0676-8 |
| ISSN: | 0188-7009 |
| ISSN: | 1661-4909 |
| Title of parent work (English): | Advances in applied Clifford algebras |
| Publisher: | Springer |
| Place of publishing: | Basel |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2017 |
| Publication year: | 2017 |
| Release date: | 2020/04/20 |
| Tag: | Clifford algebra; Dirac operator; Fredholm operators; Riemann-Hilbert problem |
| Volume: | 27 |
| Number of pages: | 23 |
| First page: | 931 |
| Last Page: | 953 |
| Funding institution: | Deutscher Akademischer Austauschdienst |
| Peer review: | Referiert |
| Institution name at the time of the publication: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Informatik |
