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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

Retrieve article from Numdam

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

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

Retrieve article from Numdam

XI: 01, 1-20, LNM 581 (1977)

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) $

Keywords: Harmonic functions, Real analytic functions, Completely monotonic functions

Nature: Original

Retrieve article from Numdam