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1.
Qiaofang Lian 《Mathematical Methods in the Applied Sciences》2019,42(5):1335-1351
Recently, continuous‐time nonstationary Gabor (NSG) frames were introduced in adaptive signal analysis. They allow for efficient reconstruction with flexible sampling and varying window functions. In this paper, we focus on the existence and construction of NSG frames in the discrete‐time setting. We provide existence results for painless NSG frames and for NSG frames with fast decaying window functions. We also construct NSG frames with noncompactly supported window functions from a known painless NSG frame. Some examples are provided to illustrate the general theory. 相似文献
2.
研究了在一些扰动条件下Hilbert广义框架的稳定性,得到了一些结果,这些结果是OLE Christensen关于Hilbert框架经典结果的推广。 相似文献
3.
Frames Associated with Measurable Spaces 总被引:4,自引:0,他引:4
We present two results dealing with dilation and perturbation properties of general frames, which generalize the works of several authors in the theory of discrete frames. We also study the representing measures associated with frames. In particular, we give a necessary and sufficient condition for a representing measure to be an extreme point of the set of representing measures and show how it can be used in some concrete examples. 相似文献
4.
《Mathematische Nachrichten》2018,291(4):546-555
The paper deals with approximation results with respect to the φ‐variation by means of a family of discrete operators for φ‐absolutely continuous functions. In particular, for the considered family of operators and for the error of approximation, we first obtain some estimates which are important in order to prove the main result of convergence in φ‐variation. The problem of the rate of approximation is also studied. The discrete operators that we consider are deeply connected to some problems of linear prediction from samples in the past, and therefore have important applications in several fields, such as, for example, in speech processing. Moreover such family of operators coincides, in a particular case, with the generalized sampling‐type series on a subset of the space of the φ‐absolutely continuous functions: therefore we are able to obtain a result of convergence in variation also for the generalized sampling‐type series. Some examples are also discussed. 相似文献
5.
Andrej Zlatoš 《Journal of Functional Analysis》2004,207(1):216-252
We construct non-random bounded discrete half-line Schrödinger operators which have purely singular continuous spectral measures with fractional Hausdorff dimension (in some interval of energies). To do this we use suitable sparse potentials. Our results also apply to whole line operators, as well as to certain random operators. In the latter case we prove and compute an exact dimension of the spectral measures. 相似文献
6.
We introduce the concept of weak localization for continuous frames and use this concept to define a class of weakly localized operators. This class contains many important classes of operators, including: short time Fourier transform multipliers, Calderon–Toeplitz operators, Toeplitz operators on various functions spaces, Anti-Wick operators, some pseudodifferential operators, some Calderon–Zygmund operators, and many others. In this paper, we study the boundedness and compactness of weakly localized operators. In particular, we provide a characterization of compactness for weakly localized operators in terms of the behavior of their Berezin transforms. 相似文献
7.
8.
V. A. KHATSKEVICH V.A. SENDEROV 《数学学报(英文版)》2006,22(6):1687-1694
The operator sets, which are the subject of this paper, have been studied in many papers where, under different restrictions on the generating operators, convexity, compactness in the weak operator topology, and nonemptiness were proved for sets of different classes under study. Then the results obtained were used in these papers to solve several applied problems. Namely, they played the key role in establishing the dichotomy of nonautonomous dynamical systems, with either continuous or discrete time. In the present paper, we generalize and sharpen the already known criteria and obtain several new criteria for convexity, compactness, and nonemptiness of several special operator sets. Then, using the assertions obtained, we construct examples of sets of the form under study which are nonconvex, noncompact in the weak operator topology, as well as empty, and are generated by "smooth" operators of a special class. The existence problem for such sets remained open until the authors of this paper announced some of its results. 相似文献
9.
The results provided hereby are related to the asymptotic behaviour of certain strongly continuous semigroups, which may be
expressed in terms of iterates of positive linear operators, in the sense of Altomare’s theory. We present some applications
to concrete cases involving continuous and discrete type operators, namely the Beta and the Stancu operators.
相似文献
10.
简单介绍了一些解析函数构成的Banach空间上的满等距的结果,然后刻画了多圆柱上α-Bloch空间复合算子的等距,并得到了复合算子等距的充要条件. 相似文献
11.
本文运用算子理论方法,讨论了Hilbert空间H中的子空间框架和子空间框架算子的性质,研究了子空间框架的摄动,给出了一些有意义的结果. 相似文献
12.
E. Yu. Emel'yanov U. Kohler F. Rä biger M. P. H. Wolff 《Proceedings of the American Mathematical Society》2001,129(9):2633-2642
We discuss conditions such that strong stability and strong asymptotic compactness of a (discrete or continuous) semiflow defined on a subset in the positive cone of an ordered Banach space is preserved under asymptotic domination. This is used to show that on a Banach lattice with order continuous norm strong stability and almost periodicity of a (discrete or strongly continuous) semigroup of positive operators is preserved under asymptotic domination.
13.
Monika Dörfler 《Journal of Functional Analysis》2011,260(7):1903-1924
We study families of time-frequency localization operators and derive a new characterization of modulation spaces. This characterization relates the size of the localization operators to the global time-frequency distribution. As a by-product, we obtain a new proof for the existence of multi-window Gabor frames and extend the structure theory of Gabor frames. 相似文献
14.
Jean-Pierre Antoine Pierre Vandergheynst 《Journal of Fourier Analysis and Applications》2007,13(4):369-386
We survey the construction of the continuous wavelet transform (CWT) on the twosphere. Then we discuss the discretization
of the spherical CWT, obtaining various types of discrete frames. Finally, we give some indications on the construction of
a CWT on other conic sections. 相似文献
15.
讨论单位圆盘中Dirichlet空间上Toeplitz算子的性质,给出了Dirichiet空间上以一类连续函数为符号的Toeplitz算子满足亚正规性的充分必要条件. 相似文献
16.
《Indagationes Mathematicae》2019,30(6):1006-1022
In connection with the theory of hypercyclicity of bounded linear operators and strongly continuous semigroups of operators on Banach spaces, we make several observations about the following three topics – (i) special types of orbits, (ii) the role of large subsets of , (iii) various spectral conditions – and thereby highlight some nuances of the theory. 相似文献
17.
The piecewise continuous function space is an important state space in various nonlinear problems. In this paper, we establish some new fixed point theorems for the perturbed contraction operators in piecewise continuous function spaces. Our results can be applied to various integral operators. Some previous results are improved in this literature. As applications, the existence and uniqueness of solutions of impulsive anti‐periodic boundary value problems and the Lasota–Wazewska models with delays are exhibited at last two sections. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
18.
In this paper we study the stability of(p,Y)-operator frames.We firstly discuss the relations between p-Bessel sequences(or p-frames) and(p,Y)-operator Bessel sequences(or(p,Y)-operator frames).Through defining a new union,we prove that adding some elements to a given(p,Y)-operator frame,the resulted sequence will be still a(p,Y)-operator frame.We obtain a necessary and sufficient condition for a sequence of compound operators to be a(p,Y)operator frame.Lastly,we show that(p,Y)-operator frames for X are stable under some small perturbations. 相似文献
19.
多重圆盘上的Toeplitz代数 总被引:1,自引:0,他引:1
本文研究了H~2(T~n)上由符号为本性有界可测函数的Toeplitz算子生成的C~*-代数的结构,并得到了这样的Toeplitz算子的一些谱性质. 相似文献
20.
Zen Harper 《Integral Equations and Operator Theory》2006,54(1):69-88
In this paper, we study a discrete version of the Weiss Conjecture. In Section 1 we discuss the Reproducing Kernel Thesis
and in Section 2 we introduce the operators which concern us. Section 3 shows how to relate these operators to Carleson embeddings
and weighted composition operators, so that we can apply the Carleson measure theorem to obtain conditions for boundedness
and compactness of many weighted composition operators. Section 4 contains Theorem 4.4 which is a discrete version of the
Weiss Conjecture for contraction semigroups, and finally Section 5 shows how the usual (continuous time) Weiss Conjecture
is related to the discrete version studied here; in fact they are equivalent (for scalar valued observation operators). The
main advantage of the discrete version is that it is technically simpler – the observation operators are automatically bounded
and the functional calculus can be achieved using power series. 相似文献