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A mean value theorem on bounded symmetric domains |
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| Authors: | Miroslav Englis |
| Affiliation: | MÚ AV CR, Zitná 25, 11567 Prague 1, Czech Republic |
| Abstract: | Let  be a Cartan domain of rank  and genus  and  ,  , the Berezin transform on  ; the number  can be interpreted as a certain invariant-mean-value of a function  around  . We show that a Lebesgue integrable function satisfying  ,  , must be  -harmonic. In a sense, this result is reminiscent of Delsarte's two-radius mean-value theorem for ordinary harmonic functions on the complex  -space  , but with the role of radius  played by the quantity  . |
| Keywords: | Berezin transform bounded symmetric domains invariant mean-value property |
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