On non-homogeneous Cauchy-Fueter equations and Hartogs' phenomenon in several quaternionic variables

DOI10.1016/j.geomphys.2008.04.004zbMath1149.58010OpenAlexW2024529293MaRDI QIDQ950268

Wei Wang

Publication date: 22 October 2008

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2008.04.004

zbMATH Keywords

Hartogs' phenomenonintegral representation formulaCauchy-Fueter complexassociated Laplacian of fourth ordernon-homogeneous Cauchy-Fueter equations

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Hyper-Kähler and quaternionic Kähler geometry, ``special geometry (53C26) Invariance and symmetry properties for PDEs on manifolds (58J70) Differential complexes (58J10) Overdetermined systems of PDEs with constant coefficients (35N05)

Related Items (21)

On the Hodge-type decomposition and cohomology groups of \(k\)-Cauchy-Fueter complexes over domains in the quaternionic space ⋮ Linear BVPs and SIEs for generalized regular functions in Clifford analysis ⋮ On the weighted \(L^{2}\) estimate for the \(k\)-Cauchy-Fueter operator and the weighted \(k\)-Bergman kernel ⋮ On the Cauchy-Szegő kernel for quaternion Siegel upper half-space ⋮ The tangential Cauchy-Fueter complex on the quaternionic Heisenberg group ⋮ Hartogs phenomena for discrete \(k\)-Cauchy-Fueter operators ⋮ A variational approach to the quaternionic Monge-Ampère equation ⋮ On the optimal control method in quaternionic analysis ⋮ Hartogs phenomenon for systems of differential equations ⋮ Korn's inequality and Donati's theorem for the conformal Killing operator on pseudo-Euclidean space ⋮ Theory of several paravector variables: Bochner-Martinelli formula and Hartogs theorem ⋮ Quaternionic Monge-Ampère operator for unbounded plurisubharmonic functions ⋮ Complex associated to some systems of PDE ⋮ Sub-Riemannian Geometry and Hypoelliptic Operators ⋮ Bochner-Martinelli formula for \(k\)-Cauchy-Fueter operator ⋮ Inhomogeneous Cauchy-Riemann equation in octonion space ⋮ Octonion analysis of several variables ⋮ Boundary properties for several singular integral operators in real Clifford analysis ⋮ The \(k\)-Cauchy-Fueter complex, Penrose transformation and hartogs phenomenon for quaternionic \(k\)-regular functions ⋮ The solvability of a kind of generalized Riemann-Hilbert problems on function spaces \(H_{\ast }\) ⋮ On the tangential Cauchy-Fueter operators on nondegenerate quadratic hypersurfaces in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb {H}^2}$\end{document}

Cites Work

• \(N\)-capacity, \(N\)-harmonic radius and \(N\)-harmonic transplantation
• Explicit resolutions for the complex of several Fueter operators
• Regular functions of several quaternionic variables
• Quaternionic complexes
• Hartog's phenomenon for polyregular functions and projective dimension of related modules over a polynomial ring
• Regular functions of several quaternionic variables and the Cauchy-Fueter complex
• Complexes of Dirac operators in Clifford algebras
• Analysis of Dirac systems and computational algebra.
• Non-commutative linear algebra and plurisubharmonic functions of quaternionic variables.
• Invariant resolutions for several Fueter operators
• The weyl calculus of pseudo-differential operators
• Analysis of the module determining the properties of regular functions of several quaternionic variables.
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