共查询到20条相似文献,搜索用时 0 毫秒
1.
2.
3.
4.
5.
6.
A.G Vitushkin 《Journal of Functional Analysis》1975,20(2):149-157
This article gives a survey of the study of uniform approximation by holomorphic functions on compact sets in spaces of one or more complex variables during the last two decades. 相似文献
7.
Franc Forstneric 《Journal of Geometric Analysis》1999,9(1):93-117
Let n > 1 and let
C
n
denote the complex n-dimensional Euclidean space. We prove several jet-interpolation results for nowhere degenerate entire
mappings F:C
n →C
n
and for holomorphic automorphisms of
C
n
on discrete subsets of
C
n.We also prove an interpolation theorem for proper holomorphic embeddings of Stein manifolds into
C
n.For each closed complex submanifold (or subvariety) M ⊂
C
n
of complex dimension m < n we construct a domain Ω ⊂C
n
containing M and a biholomorphic map F: Ω →
C
n
onto
C
n
with J F ≡ 1such that F(M) intersects the image of any nondegenerate entire map G:C
n−m →C
n
at infinitely many points. If m = n − 1, we construct F as above such that
C
n ∖F(M) is hyperbolic. In particular, for each m ≥ 1we construct proper holomorphic embeddings F:C
m →C
m−1
such that the complement
C
m+1 ∖F(C
m
)is hyperbolic. 相似文献
8.
Michael Cwikel Mieczyslaw Mastylo 《Proceedings of the American Mathematical Society》1996,124(4):1103-1109
It is shown that the complex interpolation spaces and do not coincide with or and also that the couple is not a Calderón couple. Similar results are also obtained for the couples and when .
9.
A polyhedral functionlp(Δn) (f). interpolating a function f, defined on a polygon Φ, is defined by a set of interpolating nodes Δn ?Φ and a partition P(Δn) of the polygon Φ into triangles with vertices at the points of Δn. In this article we will compute for convex moduli of continuity the quatities $$\begin{gathered} E (H_\Phi ^\omega ; P (\Delta _n )) = sup || f - l_{p(\Delta _n )} (f)||, \hfill \\ f \in H_\Phi ^\omega \hfill \\ \end{gathered} $$ and also give an asymptotic estimate of the quantities $$\begin{gathered} E_n (H_\Phi ^\omega ) = infinf E (H_\Phi ^\omega ; P (\Delta _n )). \hfill \\ \Delta _n P(\Delta _n ) \hfill \\ \end{gathered} $$ 相似文献
10.
It is a well-known and elementary fact that a holomorphic function on a compact complex manifold is necessarily constant. The purpose of the present article is to investigate whether, or to what extent, a similar property holds in the setting of holomorphically foliated spaces.
11.
If γ(x)=x+iA(x),tan ?1‖A′‖∞<ω<π/2,S ω 0 ={z∈C}| |argz|<ω, or, |arg(-z)|<ω} We have proved that if φ is a holomorphic function in S ω 0 and \(\left| {\varphi (z)} \right| \leqslant \frac{C}{{\left| z \right|}}\) , denotingT f (z)= ∫?(z-ζ)f(ζ)dζ, ?f∈C 0(γ), ?z∈suppf, where Cc(γ) denotes the class of continuous functions with compact supports, then the following two conditions are equivalent:
- T can be extended to be a bounded operator on L2(γ);
- there exists a function ?1 ∈H ∞(S ω 0 ) such that ?′1(z)=?(z)+?(-z), ?z∈S ω 0 ?z∈S w 0 .
12.
13.
We study the closure in the Hardy space or the disk algebra of algebras generated by two bounded functions, one of which is
a finite Blaschke product. We give necessary and sufficient conditions for density or finite codimension (of the closure)
of such algebras. The conditions are expressed in terms of the inner part of a certain function which is explicitly derived
from each pair of generators. Our results are based on identifyingz-invariant subspaces included in the closure of the algebra.
The second-named author thanks the University at Albany, Harvard University, and Brown University for their hospitality during
the completion of this work. 相似文献
14.
V. V. Savchuk 《Ukrainian Mathematical Journal》2007,59(9):1397-1407
We investigate the problem of approximation of functions ƒ holomorphic in the unit disk by means A
ρ, r
(f) as ρ → 1−. In terms of the error of approximation by these means, a constructive characteristic of classes of holomorphic
functions H
p
r
Lipα is given. The problem of the saturation of A
ρ, r
(f) in the Hardy space H
p
is solved.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 9, pp. 1253–1260, September, 2007. 相似文献
15.
V. V. Savchuk 《Ukrainian Mathematical Journal》2007,59(8):1163-1183
We establish necessary and sufficient conditions under which a real-valued function from
, 1 ≤ p < ∞, is badly approximable by the Hardy subspace H
p
0
:= {ƒ ∈ H
p
: ƒ(0) = 0}. In a number of cases, we obtain the exact values of the best approximations in the mean of functions holomorphic
in the unit disk by functions holomorphic outside this disk. We use the obtained results for finding the exact values of the
best polynomial approximations and n-widths of some classes of holomorphic functions. We establish necessary and sufficient conditions under which the generalized
Bernstein inequality for algebraic polynomials on the unit circle is true.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 8, pp. 1047–1067, August, 2007. 相似文献
16.
17.
18.
19.
Abstract. Let be open,X a Banach space and . We show that every is holomorphic if and only if every set inX is bounded. Things are different if we assume f to be locally bounded. Then we show that it suffices that is holomorphic for all , where W is a separating subspace of to deduce that f is holomorphic. Boundary Tauberian convergence and membership theorems are proved. Namely, if boundary values (in a weak
sense) of a sequence of holomorphic functions converge/belong to a closed subspace on a subset of the boundary having positive
Lebesgue measure, then the same is true for the interior points of , uniformly on compact subsets. Some extra global majorants are requested. These results depend on a distance Jensen inequality.
Several examples are provided (bounded and compact operators; Toeplitz and Hankel operators; Fourier multipliers and small
multipliers).
Received January 29, 1998; in final form March 8, 1999 / Published online May 8, 2000 相似文献
20.
A natural interpolation problem in the cone of positive harmonicfunctions is considered and the corresponding interpolatingsequences are geometrically described. 相似文献