Displaying similar documents to “A generalization of Fueter’s monogenic functions to fine domains”

Finely differentiable monogenic functions

Roman Lávička (2006)

Archivum Mathematicum

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Since 1970’s B. Fuglede and others have been studying finely holomorhic functions, i.e., ‘holomorphic’ functions defined on the so-called fine domains which are not necessarily open in the usual sense. This note is a survey of finely monogenic functions which were introduced in (Lávička, R., A generalisation of monogenic functions to fine domains, preprint.) like a higher dimensional analogue of finely holomorphic functions.

On the axiomatic of harmonic functions II

Corneliu Constantinescu, A. Cornea (1963)

Annales de l'institut Fourier

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On démontre dans l’axiomatique de M. Brelot la linéarité de l’opération de balayage appliquée aux fonctions surharmoniques en utilisant seulement les axiomes 1, 2, 3, l’espace de base n’ayant pas nécessairement une base dénombrable.

Vector-valued holomorphic and harmonic functions

Wolfgang Arendt (2016)

Concrete Operators

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Holomorphic and harmonic functions with values in a Banach space are investigated. Following an approach given in a joint article with Nikolski [4] it is shown that for bounded functions with values in a Banach space it suffices that the composition with functionals in a separating subspace of the dual space be holomorphic to deduce holomorphy. Another result is Vitali’s convergence theorem for holomorphic functions. The main novelty in the article is to prove analogous results for harmonic...

Multiply superharmonic functions

Kohur Gowrisankaran (1975)

Annales de l'institut Fourier

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Some results concerning the multiply superharmonic functions and the boundary behaviour are given and some problems involving these notions are described.