共查询到20条相似文献,搜索用时 0 毫秒
1.
《Mathematische Nachrichten》2017,290(8-9):1374-1380
For open sets we study Hadamard operators on , that is, continuous linear operators which admit all monomials as eigenvectors. We characterize them as operators of the form where T is a distribution and ⋆ the multiplicative convolution. This extends previous results for the case of but requires essentially different methods. 相似文献
2.
3.
Compact Operators on Bergman Spaces 总被引:2,自引:0,他引:2
We prove that a bounded operator S on L
a
p
for p > 1 is compact if
and only if the Berezin transform of S vanishes on the boundary of the unit
disk if S satisfies some integrable conditions. Some estimates about the norm
and essential norm of Toeplitz operators with symbols in BT are obtained. 相似文献
4.
It is known that for particular classes of operators on certain reproducing
kernel Hilbert spaces, key properties of the operators (such as boundedness
or compactness) may be determined by the behaviour of the operators
on the reproducing kernels. We prove such results for Toeplitz operators on
the Paley-Wiener space, a reproducing kernel Hilbert space over
. Namely,
we show that the norm of such an operator is equivalent to the supremum of
the norms of the images of the normalised reproducing kernels of the space.
In particular, therefore, the operator is bounded exactly when this supremum
is finite. In addition, a counterexample is provided which shows that the operator
norm is not equivalent to the supremum of the norms of the images
of the real normalised reproducing kernels. We also give a necessary and
sufficient condition for compactness of the operators, in terms of their limiting
behaviour on the reproducing kernels. 相似文献
5.
Products of Toeplitz Operators on the Bergman Space 总被引:1,自引:0,他引:1
Issam Louhichi Elizabeth Strouse Lova Zakariasy 《Integral Equations and Operator Theory》2006,54(4):525-539
In 1962 Brown and Halmos gave simple conditions for the product of two Toeplitz operators on Hardy space to be equal to a
Toeplitz operator. Recently, Ahern and Cucković showed that a similar result holds for Toeplitz operators with bounded harmonic
symbols on Bergman space. For general symbols, the situation is much more complicated. We give necessary and sufficient conditions
for the product to be a Toeplitz operator (Theorem 6.1), an explicit formula for the symbol of the product in certain cases
(Theorem 6.4), and then show that almost anything can happen (Theorem 6.7). 相似文献
6.
It is shown that if ϕ is a univalent self-map on the unit disk
is not an automorphism and has a fixed point in
and if the essential spectral radius of the composition operator Cϕ on H2 is different from zero, then the spectrum of Cϕ on BMOA coincides with
This answers in the affirmative a conjecture by MacCluer and Saxe. 相似文献
7.
We consider hypercyclic composition operators on
which can be obtained from the translation operator using polynomial automorphisms of
. In particular we show that if C
S
is a hypercyclic operator for an affine automorphism S on
, then
for some polynomial automorphism Θ and vectors a and b, where I is the identity operator. Finally, we prove the hypercyclicity of “symmetric translations” on a space of symmetric analytic
functions on ℓ1.
Received: 8 June 2006 Revised: 26 September 2006 相似文献
8.
We study convolution operators in Bessel potential spaces and (fractional) Sobolev spaces over a finite interval. The main purpose of the investigation is to find conditions on the convolution kernel or on a Fourier symbol of these operators under which the solutions inherit higher regularity from the data. We provide conditions which ensure the transmission property for the finite interval convolution operators between Bessel potential spaces and Sobolev spaces. These conditions lead to smoothness preserving properties of operators defined in the above-mentioned spaces where the kernel, cokernel and, therefore, indices do not depend on the order of differentiability. In the case of invertibility of the finite interval convolution operator, a representation of its inverse is presented in terms of the canonical factorization of a related Fourier symbol matrix function. 相似文献
9.
Stephen M. Buckley M. S. Ramanujan Dragan Vukotić 《Integral Equations and Operator Theory》1999,35(1):1-19
This paper studies the boundedness and compactness of the coefficient multiplier operators between various Bergman spacesA
p
and Hardy spacesH
q
. Some new characterizations of the multipliers between the spaces with exponents 1 or 2 are derived which, in particular, imply a Bergman space analogue of the Paley-Rudin Theorem on sparse sequences. Hardy and Bergman spaces are shown to be linked using mixed-norm spaces, and this linkage is used to improve a known result on (A
p
,A
2), 1<p<2.Compact (H
1,H
2) and (A
1,A
2) multipliers are characterized. The essential norms and spectra of some multiplier operators are computed. It is shown that forp>1 there exist bounded non-compact multiplier operators fromA
p
toA
q
if and only ifpq. 相似文献
10.
In the case of radial symbols we study the behavior of different properties (boundedness, compactness, spectral properties, etc.) of Toeplitz operators Ta() acting on weighted Bergman spaces
over the unit disk
, in dependence on , and compare their limit behavior under
with corresponding properties of the initial symbol a. 相似文献
11.
M. Jasiczak 《Archiv der Mathematik》2006,87(5):436-448
We study regularity of Bergman and Szeg? projections on Sobolev type weighted-sup spaces. The paper covers the case of strongly
pseudoconvex domains with C4 boundary and, partially, domains of finite type in the sense of D’Angelo.
Received: 6 October 2005 相似文献
12.
We prove analogues of the Brown-Halmos and Nehari theorems on
the norms of Toeplitz and Hankel operators, respectively, acting on subspaces
of Hardy type of reflexive rearrangement-invariant spaces with nontrivial Boyd
indices. 相似文献
13.
Vladimir S. Rabinovich Steffen Roch John Roe 《Integral Equations and Operator Theory》2004,49(2):221-238
The Fredholmness of a band-dominated operator on
is closely
related with the invertibility of its limit operators: the operator is Fredholm if
and only if each of its limit operators is invertible and if the norms of their inverses
are uniformly bounded. The goal of the present note is to show how the
Fredholm index of a Fredholm band-dominated operator can be determined
in terms of its limit operators. 相似文献
14.
Maribel Loaiza Marcos López-García Salvador Pérez-Esteva 《Integral Equations and Operator Theory》2005,53(2):287-296
In this paper we decompose
into diadic annuli
and consider the class Sp,q of Toeplitz operators Tφ for which the sequence of Schatten norms
belongs to ℓq, where φn = φχ An. We study the boundedness and compactness of the operators in Sp,q and we describe the operators Tφ , φ ≥ 0 in these spaces in terms of weighted Herz norms of the averaging operator of the symbols φ. 相似文献
15.
Sobolev spaces on an arbitrary metric space 总被引:15,自引:0,他引:15
Piotr Hajłasz 《Potential Analysis》1996,5(4):403-415
We define Sobolev space W
1,p
for 1<p on an arbitrary metric space with finite diameter and equipped with finite, positive Borel measure. In the Euclidean case it coincides with standard Sobolev space. Several classical imbedding theorems are special cases of general results which hold in the metric case. We apply our results to weighted Sobolev space with Muckenhoupt weight.This work is supported by KBN grant no. 2 1057 91 01 相似文献
16.
We characterize a property that is useful for constructing large spaces of universal functions in a wide variety of settings.
In particular, we show that given any sequence of automorphisms of the ball that admits a universal function , there exists a closed infinite dimensional subspace, generated by inner functions, that is isometric to . We put our results in the context of bounded symmetric domains. 相似文献
17.
The invertible, compact and Fredholm multiplication operators on Orlicz spaces are characterized in this paper. 相似文献
18.
Compact and weakly compact weighted composition operators on weighted spaces of continuous functions
In this note we characterize the compact and weakly compact weighted composition operatorsW
, on certain weighted locally convex spacesCV
o(X, E) of vector-valued continuous functions induced by self maps ofX and the operator-valued mappings XB(E).The work of this author was supported in part by CSIR Grant 9/100/92-EMR-IThe work of this author was supported in part by UGC Grant F.8-7/91 (RBB-II) 相似文献
19.
Generalized Anti-Wick operators are introduced as a class of
pseudodifferential operators which depend on a symbol and two different window
functions. Using symbols in Sobolev spaces with negative smoothness and
windows in so-called modulation spaces, we derive new conditions for the
boundedness on L2 of such operators and for their membership in the Schatten
classes. These results extend and refine results contained in [20], [10], [5],
[4], and [14]. 相似文献
20.
Zhijian Wu 《Integral Equations and Operator Theory》1996,24(3):352-371
We study the commutator of the multiplication and harmonic Bergman projection, Hankel and Toeplitz operators on the harmonic Bergman spaces. The same type operators have been well studied on the analytic Bergman spaces. The main difficulty of this study is that the bounded harmonic function space is not an algebra! In this paper, we characterize theL
p boundedness and compactness of these operators with harmonic symbols. Results about operators in Schatten classes, the cut-off phenomenon and general symbols are also included.Partially supported by a grant from the Research Grants Committee of the University of Alabama. 相似文献