An extension theorem for holomorphic functions of slow growth on covering spaces of projective manifolds

1995 ◽  
Vol 5 (2) ◽  
pp. 281-291 ◽  
Author(s):  
Finnur Lárusson
Keyword(s):  
Slow Growth ◽  
Extension Theorem ◽  
Holomorphic Functions ◽  
Covering Spaces ◽  
Projective Manifolds

scholarly journals Ambiguous points of holomorphic functions of slow growth.

1971 ◽  
Vol 18 (2) ◽  
pp. 161-168
Author(s):  
R. L. Hall
Keyword(s):  
Slow Growth ◽  
Holomorphic Functions

scholarly journals Holomorphic extension of generalizations ofHpfunctions

1985 ◽  
Vol 8 (3) ◽  
pp. 417-424 ◽  
Author(s):  
Richard D. Carmichael
Keyword(s):  
Convex Hull ◽  
Extension Theorem ◽  
Holomorphic Functions ◽  
Holomorphic Extension ◽  
Finite Union ◽  
Convex Cones ◽  
Recent Analysis ◽  
Boundary Values ◽  
Connected Component ◽  
Open Convex

In recent analysis we have defined and studied holomorphic functions in tubes inℂnwhich generalize the HardyHpfunctions in tubes. In this paper we consider functionsf(z),z=x+iy, which are holomorphic in the tubeTC=ℝn+iC, whereCis the finite union of open convex conesCj,j=1,…,m, and which satisfy the norm growth of our new functions. We prove a holomorphic extension theorem in whichf(z),z ϵ TC, is shown to be extendable to a function which is holomorphic inT0(C)=ℝn+i0(C), where0(C)is the convex hull ofC, if the distributional boundary values in𝒮′off(z)from each connected componentTCjofTCare equal.

scholarly journals The Ohsawa-Takegoshi Extension Theorem on Some Unbounded Sets

2007 ◽  
Vol 188 ◽  
pp. 19-30 ◽  
Author(s):  
Żywomir Dinew
Keyword(s):  
Bergman Spaces ◽  
Extension Theorem ◽  
Holomorphic Functions ◽  
Pseudoconvex Domains

AbstractWe use a method of Berndtsson to obtain a simplification of Ohsawa’s result concerning extension of L2-holomorphic functions. We also study versions of the Ohsawa-Takegoshi theorem for some unbounded pseudoconvex domains, with an application to the theory of Bergman spaces. Using these methods we improve some constants, that arise in related inequalities.

scholarly journals On the extension of L2 holomorphic functions V-Effects of generalization

2001 ◽  
Vol 161 ◽  
pp. 1-21 ◽  
Author(s):  
Takeo Ohsawa
Keyword(s):  
Extension Theorem ◽  
Holomorphic Functions ◽  
Extension Theory ◽  
Holomorphic Bundle

A general extension theorem for L2 holomorphic bundle-valued top forms is formulated. Although its proof is based on a principle similar to Ohsawa-Takegoshi’s extension theorem, it explains previous L2 extendability results systematically and bridges extension theory and division theory.

ON THE OPTIMAL EXTENSION THEOREM AND A QUESTION OF OHSAWA

2020 ◽  
pp. 1-12
Author(s):  
SHA YAO ◽  
ZHI LI ◽  
XIANGYU ZHOU
Keyword(s):  
Natural Condition ◽  
Extension Theorem ◽  
Holomorphic Functions ◽  
Main Application ◽  
Optimal Extension

Abstract In this paper, we present a version of Guan-Zhou’s optimal $L^{2}$ extension theorem and its application. As a main application, we show that under a natural condition, the question posed by Ohsawa in his series paper VIII on the extension of $L^{2}$ holomorphic functions holds. We also give an explicit counterexample which shows that the question fails in general.

Some results of Lindelöf type involving the segmental behaviour of holomorphic functions

1993 ◽  
Vol 114 (1) ◽  
pp. 57-65 ◽  
Author(s):  
Francisca Bravo ◽  
Daniel Girela
Keyword(s):  
Analytic Function ◽  
Unit Disc ◽  
Slow Growth ◽  
Holomorphic Functions ◽  
Maximum Modulus ◽  
Classical Theorem ◽  
Asymptotic Value

AbstractA classical theorem of Lindelöf asserts that if ƒ is a function analytic and bounded in the unit disc δ which has the asymptotic value L at a point ξ ε ∂ δ then it has the non-tangential limit L at ξ. This result does not remain true for functions f analytic in δ whose maximum modulus grows to infinity arbitrarily slowly. However, the second author has recently obtained some results of Lindelöf type valid for these functions. In this paper we obtain new results of this kind. We prove that if f is an analytic function of slow growth in δ and ξ ε ∂ δ, then certain restrictions on the growth of ƒ′ along a segment which ends at ξ do imply that ƒ has a non-tangential limit at ξ.

scholarly journals Holomorphic functions of slow growth on coverings of pseudoconvex domains in Stein manifolds

2006 ◽  
Vol 142 (04) ◽  
pp. 1018-1038 ◽  
Author(s):  
Alexander Brudnyi
Keyword(s):  
Slow Growth ◽  
Holomorphic Functions ◽  
Pseudoconvex Domains ◽  
Stein Manifolds

Structure of a foliated neighbourhood

1976 ◽  
Vol 79 (1) ◽  
pp. 101-110 ◽  
Author(s):  
Jenny Harrison
Keyword(s):  
Fibre Bundle ◽  
Extension Theorem ◽  
Holonomy Group ◽  
Structure Group ◽  
Compact Leaf ◽  
Discrete Structure ◽  
Covering Spaces

C. Ehresmann (2) has shown that if a leaf L of a smooth foliation has a foliated neighbourhood, then there exists a fibre bundle over L, normal to the leaves, with discrete structure group. Using the concept of a microbundle and the n-isotopy extension theorem, we find a similar result for both PL and TOP categories, and, in addition, show that the structure group can be chosen to be the holonomy group of L. As for applications we show that holonomy characterizes the foliated neighbourhood of a leaf (proved by Haefliger in the differentiable case (3)). In particular, if the holonomy group of a compact leaf L is trivial then the leaf has a trivial foliated neighbourhood, and if it is finite it has a neighbourhood of compact leaves which are covering spaces of L. Another corollary is the known result that a proper submersion with compact fibre is a fibration. Finally we use the fact that the constructed normal microbundle can be chosen to have its fibres contained in the leaves of a transverse foliation to demonstrate isotopy uniqueness of normal microbundles.

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