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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-monogenic operators

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

Czechoslovak Mathematical Journal

In this paper we consider operators acting on a subspace of the space L 2 ( m ; m ) of square integrable functions and, in particular, Clifford differential operators with polynomial coefficients. The subspace is defined as the orthogonal sum of spaces s , k of specific Clifford basis functions of L 2 ( m ; m ) . Every Clifford endomorphism of 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...

Closed universal subspaces of spaces of infinitely differentiable functions

Stéphane Charpentier, Quentin Menet, Augustin Mouze (2014)

Annales de l’institut Fourier

We exhibit the first examples of Fréchet spaces which contain a closed infinite dimensional subspace of universal series, but no restricted universal series. We consider classical Fréchet spaces of infinitely differentiable functions which do not admit a continuous norm. Furthermore, this leads us to establish some more general results for sequences of operators acting on Fréchet spaces with or without a continuous norm. Additionally, we give a characterization of the existence of a closed subspace...

Cluster sets of analytic multivalued functions

S. Harbottle (1992)

Studia Mathematica

Classical theorems about the cluster sets of holomorphic functions on the unit disc are extended to the more general setting of analytic multivalued functions, and examples are given to show that these extensions cannot be improved.

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