Spherical monogenic functions and analytic functionals on the unit sphere

DOI10.3836/tjm/1270215166zbMath0481.30040OpenAlexW1983527220MaRDI QIDQ1161843

Fransiscus Sommen

Publication date: 1981

Published in: Tokyo Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3836/tjm/1270215166

zbMATH Keywords

spherical harmonicsfunction theory in Clifford algebrasspherical Cauchy-Riemann operatorTaylor and Laurent expansions

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Spaces of bounded analytic functions of one complex variable (30H05) Boundary value problems in the complex plane (30E25) Hilbert spaces of continuous, differentiable or analytic functions (46E20) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Spherical harmonics (33C55)

Related Items (23)

Clifford analysis with generalized elliptic and quasi elliptic functions ⋮ Some properties of a kind of generalized Teodorescu operator in Clifford analysis ⋮ Special functions in Clifford analysis and axial symmetry ⋮ Applications of complex Clifford analysis to the study of solutions to generalized Dirac and Klein-Gordon equations with holomorphic potentials ⋮ Spherical \(\Pi \)-type operators in Clifford analysis and applications ⋮ The Radon transform between monogenic and generalized slice monogenic functions ⋮ Spinor-valued \(L^2\)-spaces on \(S^{m-1}\) and representations of \(\mathrm{Spin}^+(1,m)\) ⋮ Approximation of monogenic functions by higher order Szegő kernels on the unit ball and half space ⋮ Orthogonal basis for spherical monogenics by step two branching ⋮ Polyakov spin factors and Laplacians on homogeneous spaces ⋮ Inversions for the Hua-Radon and the polarized Hua-Radon transform ⋮ Monogenic differential operators ⋮ Szegö-Radon transform for biaxially monogenic functions ⋮ Runge approximation theorems in complex Clifford analysis together with some of their applications ⋮ Spherical monogenics on the Lie sphere ⋮ Unnamed Item ⋮ On the harmonic and monogenic decomposition of polynomials ⋮ Some properties of quasi-Cauchy-type singular integral operator on unbounded domains ⋮ Rarita–Schwinger fields in the half space ⋮ Vekua-type systems related to two-sided dual \(k\)-hypermonogenic functions ⋮ Series expansions and maximum principles for generalized analytic vectors in the spaceRn ⋮ Duality in complex Clifford analysis ⋮ The Paley-Wiener theorem in \(\mathbb{R}^n\) with the Clifford analysis setting

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