Riemann–Hilbert Problems for Axially Symmetric Null-Solutions to Iterated Generalised Cauchy–Riemann Equations in Rn+1

The Riemann–Hilbert boundary value problems with Clifford-algebra valued variable coefficients for null-solutions to iterated generalised Cauchy–Riemann equations, which are also so-called poly-monogenic functions, defined over axial symmetric domains of R n + 1 , are studied in this context. The in...

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Bibliographic Details
Published in:The Journal of geometric analysis 2024, Vol.34 (2)
Main Authors: He, Fuli, Huang, Qian, Ku, Min
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Boundary value problems
Cauchy-Riemann equations
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Mathematical analysis
Mathematics
Mathematics and Statistics
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Summary:The Riemann–Hilbert boundary value problems with Clifford-algebra valued variable coefficients for null-solutions to iterated generalised Cauchy–Riemann equations, which are also so-called poly-monogenic functions, defined over axial symmetric domains of R n + 1 , are studied in this context. The integral representation solutions to such problems and their solvable conditions are given. Here, the idea of ours is to use the Fischer decomposition theorems for poly-monogenic functions considered. As an application, the solutions to a Schwarz problem are derived too. Then, the results obtained are extended to axially symmetric null-solutions to perturbed iterated generalised Cauchy–Riemann equations.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-023-01509-1