Zobrazeno 1 - 10
of 96
pro vyhledávání: '"Poletsky, Evgeny A."'
Autor:
Poletsky, Evgeny A.
In this paper we prove the basic facts for pluricomplex Green functions on manifolds. The main goal is to establish properties of complex manifolds that make them analogous to relatively compact or hyperconvex domains in Stein manifolds. The final ve
Externí odkaz:
http://arxiv.org/abs/1904.03267
Autor:
Poletsky, Evgeny A.
Using pluricomplex Green functions we introduce a compactification of a complex manifold $M$ invariant with respect to biholomorphisms similar to the Martin compactification in the potential theory. For this we show the existence of a norming volume
Externí odkaz:
http://arxiv.org/abs/1812.09277
Let $M$ be a complex manifold and $PSH^{cb}(M)$ be the space of bounded continuous plurisubharmonic functions on $M$. In this paper we study when functions from $PSH^{cb}(M)$ separate points. Our main results show that this property is equivalent to
Externí odkaz:
http://arxiv.org/abs/1712.02005
Autor:
Dharmasena, Dayal, Poletsky, Evgeny A.
Let $W$ be a domain in a connected complex manifold $M$ and $w_0\in W$. Let ${\mathcal A}_{w_0}(W,M)$ be the space of all continuous mappings of a closed unit disk $\overline D$ into $M$ that are holomorphic on the interior of $\overline D$, $f(\part
Externí odkaz:
http://arxiv.org/abs/1708.04530
Autor:
Poletsky, Evgeny A.
In this paper we show that that on a strongly pseudoconvex domain $D$ the projective limit of all Poletsky--Stessin Hardy spaces $H^p_u(D)$, introduced in \cite{PS}, is isomorphic to the space $H^\infty(D)$ of bounded holomorphic functions on $D$ end
Externí odkaz:
http://arxiv.org/abs/1503.00575
Autor:
Poletsky, Evgeny A., Shrestha, Khim R.
In this paper we completely characterize those weighted Hardy spaces that are Poletsky--Stessin Hardy spaces $H^p_u$. We also provide a reduction of $H^\infty$ problems to $H^p_u$ problems and demonstrate how such a reduction can be used to make shor
Externí odkaz:
http://arxiv.org/abs/1503.00535
Autor:
Dharmasena, Dayal, Poletsky, Evgeny A.
Let $(W,\Pi)$ be a Riemann domain over a complex manifold $M$ and $w_0$ be a point in $W$. Let $\mathbb D$ be the unit disk in $\mathbb C$ and $\mathbb T=\bd\mathbb D$. Consider the space ${\mathcal S}_{1,w_0}({\bar{\mathbb D}},W,M)$ of continuous ma
Externí odkaz:
http://arxiv.org/abs/1210.1191
Autor:
Larusson, Finnur, Poletsky, Evgeny A.
We prove a disc formula for the largest plurisubharmonic subextension of an upper semicontinuous function on a domain $W$ in a Stein manifold to a larger domain $X$ under suitable conditions on $W$ and $X$. We introduce a related equivalence relation
Externí odkaz:
http://arxiv.org/abs/1201.5875
Autor:
Poletsky, Evgeny A.
In this paper we provide sufficient conditions for the graphs of holomorphic mappings on compact sets in complex manifolds to have Stein neighborhoods. We show that under these conditions the mappings have properties analogous to properties of holomo
Externí odkaz:
http://arxiv.org/abs/1107.5034
Autor:
Poletsky, Evgeny A.
The classical results about the boundary values of holomorphic or harmonic functions on a domain $D$ state that under additional integrability assumptions these functions have limits along specific sets approaching boundary. The proofs of these resul
Externí odkaz:
http://arxiv.org/abs/1105.1365