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Canonical bases for $𝔰𝔩 (2, ℂ)$ -modules of spherical monogenics in dimension 3

Roman Lávička (2010)

Archivum Mathematicum

Spaces of homogeneous spherical monogenics in dimension 3 can be considered naturally as $𝔰𝔩 (2, ℂ)$ -modules. As finite-dimensional irreducible $𝔰𝔩 (2, ℂ)$ -modules, they have canonical bases which are, by construction, orthogonal. In this note, we show that these orthogonal bases form the Appell system and coincide with those constructed recently by S. Bock and K. Gürlebeck in [3]. Moreover, we obtain simple expressions of elements of these bases in terms of the Legendre polynomials.

Carleson measure and monogenic functions

S. Bernstein, P. Cerejeiras (2007)

Studia Mathematica

We present necessary and sufficient conditions for a measure to be a p-Carleson measure, based on the Poisson and Poisson-Szegő kernels of the n-dimensional unit ball.

Cauchy-Kowalewski extension theorems and representations of analytic functionals acting over special classes of real n-dimensional submanifolds of $C^{(} n + 1)$

Ryan, John (1984)

Proceedings of the 11th Winter School on Abstract Analysis

Cauchy-Kowalewski theorems in Clifford analysis : a survey

Brackx, F., Delanghe, R., Sommen, F. (1984)

Proceedings of the 11th Winter School on Abstract Analysis

Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space.

Brackx, Fred, De Schepper, Nele, Sommen, Frank (2004)

International Journal of Mathematics and Mathematical Sciences

Clifford analysis approach to a self-conjugate Cauchy type integral on Ahlfors regular surfaces

Ricardo Abreu Blaya, Juan Bory Reyes (2014)

Annales Polonici Mathematici

In this note, based on a natural isomorphism between the spaces of differential forms and Clifford algebra-valued multi-vector functions, the Cauchy type integral for self-conjugate differential forms in ℝⁿ is considered.

Clifford and harmonic analysis on cylinders and torii.

Rolf Sören Krausshar, John Ryan (2005)

Revista Matemática Iberoamericana

Cotangent type functions in Rn are used to construct Cauchy kernels and Green kernels on the conformally flat manifolds Rn/Zk where 1 < = k ≤ M. Basic properties of these kernels are discussed including introducing a Cauchy formula, Green's formula, Cauchy transform, Poisson kernel, Szegö kernel and Bergman kernel for certain types of domains. Singular Cauchy integrals are also introduced as are associated Plemelj projection operators. These in turn are used to study Hardy spaces in this...

Clifford-Hermite Wavelets in Euclidean Space.

F. Brackx, F. Sommen (2000)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

Clifford-Hermite-monogenic operators

Freddy Brackx, Nele de Schepper, Frank Sommen (2006)

Czechoslovak Mathematical Journal

In this paper we consider operators acting on a subspace $ℳ$ of the space $L_{2} (ℝ^{m}; ℂ_{m})$ of square integrable functions and, in particular, Clifford differential operators with polynomial coefficients. The subspace $ℳ$ is defined as the orthogonal sum of spaces $ℳ_{s, k}$ of specific Clifford basis functions of $L_{2} (ℝ^{m}; ℂ_{m})$ . Every Clifford endomorphism of $ℳ$ can be decomposed into the so-called Clifford-Hermite-monogenic operators. These Clifford-Hermite-monogenic operators are characterized in terms of commutation relations and they...

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