An extremal plurisubharmonic function associated to a convex pluricomplex Green function with pole at infinity.
Plurisubharmonic saddles
A certain linear growth of the pluricomplex Green function of a bounded convex domain of at a given boundary point is related to the existence of a certain plurisubharmonic function called a “plurisubharmonic saddle”. In view of classical results on the existence of angular derivatives of conformal mappings, for the case of a single complex variable, this allows us to deduce a criterion for the existence of subharmonic saddles.
Partial differential operators of infinite order with constant coefficients on the space of analytic functions on the polydisc
Solution operators for convolution equations on the germs of analytic functions on compact convex sets in
is compact and convex it is known for a long time that the nonzero constant coefficients linear partial differential operators (of finite or infinite order) are surjective on the space of all analytic functions on G. We consider the question whether solutions of the inhomogeneous equation can be given in terms of a continuous linear operator. For instance we characterize those sets G for which this is always the case.
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