Author:
Biard Séverine,Fornæss John Erik,Wu Jujie
Abstract
AbstractWe study the density of polynomials in $$H^2(E,\varphi )$$
H
2
(
E
,
φ
)
, the space of square integrable functions with respect to $$\mathrm{e}^{-\varphi }\mathrm{d}m$$
e
-
φ
d
m
and holomorphic on the interior of E in $${\mathbb {C}}$$
C
, where $$\varphi $$
φ
is a subharmonic function and dm is a measure on E. We give a result where E is the union of a Lipschitz graph and a Carathéodory domain, which we state as a weighted $$L^2$$
L
2
-version of the Mergelyan theorem. We also prove a weighted $$L^2$$
L
2
-version of the Carleman theorem.
Funder
NTNU Norwegian University of Science and Technology
Publisher
Springer Science and Business Media LLC
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