I: 01, 3-17, LNM 39 (1967)
AVANISSIAN, Vazgain
Sur l'harmonicité des fonctions séparément harmoniques (Potential theory)
This paper proves a harmonic version of Hartogs' theorem: separately harmonic functions are jointly harmonic (without any boundedness assumption) using a complex extension procedure. The talk is an extract from the author's original work in Ann. ENS, 178, 1961
Comment: This talk was justified by the current interest of the seminar in doubly excessive functions, see Cairoli 102 in the same volume
Keywords: Doubly harmonic functions
Nature: Exposition
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XI: 01, 1-20, LNM 581 (1977)
AVANISSIAN, Vazgain
Fonctions harmoniques d'ordre infini et l'harmonicité réelle liée à l'opérateur laplacien itéré (Potential theory, Miscellanea)
This paper studies two classes of functions in (an open set of) $R^n$, $n\ge1$: 1) Harmonic functions of infinite order (see Avanissian and Fernique, Ann. Inst. Fourier, 18-2, 1968), which are $C^\infty$ functions satisfying a growth condition on their iterated laplacians, and are shown to be real analytic. 2) Infinitely differentiable functions (or distributions) similar to completely monotonic functions on the line, i.e., whose iterated laplacians are alternatively positive and negative (they were introduced by Lelong). Among the results is the fact that the second class is included in the first
Keywords: Harmonic functions, Real analytic functions, Completely monotonic functions
Nature: Original
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