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广义框架的一些等式和不等式 总被引:1,自引:0,他引:1
广义框架是框架的推广,它包含了Hilbert空间中通常框架的最近各种拓广.建立广义框架的一些等式和不等式.所得结果推广和改进了Balan R.,Casazza P G.,Edidin D.和Kutyniok G.的结果.特别地,说明了不等式中的界是最佳的. 相似文献
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《数学的实践与认识》2020,(2)
研究希尔伯特空间中向量值调制框架的特征.给出函数族{E_(mb)S_(na)h}_(m,n∈Z~2)构成空间L~2(R~2,C~s)的向量值调制框架的充分条件和{E_(mb)S_(na)h}_(m,n∈Z~2)成为向量值调制紧框架的等价条件. 相似文献
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本文运用算子理论方法,讨论了Hilbert 空间$H$中$g$-框架和$g$-框架算子的性质; 并且研究了$g$-框架的扰动,给出了一些有意义的结果. 相似文献
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Di-Rong Chen 《Journal of Approximation Theory》2000,107(2):204
This note studies Bessel sequences and frames of shift-invariant spaces generated by a countable set of periodic functions. We give characterizations under which the set of translations of the countable set is a Bessel sequence or a frame in terms of spectral decompositions of some self-adjoint operators. 相似文献
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本文首先给出了希尔伯特空间H上两个半小波框架序列成为小波框架的一个充分条件,该结论与框架的扰动理论有关.然后建立了通过膨胀与平移母函数生成L~2(R)上的小波框架的膨胀参数,平移参数以及母函数的一些充分条件.这些结果推广了小波框架理论中经典文献中的相关结论.我们还对贝塞尔序列进行了讨论,并得到了一些有趣的结论. 相似文献
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The objective of this paper is to investigate the question of modifying a given generalized Bessel sequence to yield a generalized frame or a tight generalized frame by finite extension. Some necessary and sufficient conditions for the finite extensions of generalized Bessel sequences to generalized frames or tight generalized frames are provided, and every result is illustrated by the corresponding example. 相似文献
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姚喜妍 《应用泛函分析学报》2008,10(2):155-161
引入并研究了Banach空间X中的Bessel集、广义框架与广义Riesz基.对X中的任一Bessel集{gm}m∈M,定义有界线性算子T:L^2(P)→X^*,利用算子丁,给出了Bessel集与广义框架的等价刻画.同时讨论了广义框架和广义Riesz基的摄动. 相似文献
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Bessel sequence plays an important role in the study of frames for a Hilbert space with the convergence of a frame series, which has been widely studied in the literature. This paper addresses multi-wavelet Bessel sequences in Sobolev spaces setting, the result obtained is useful for the study of multi-wavelet frames in these spaces. 相似文献
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Expansion of frames to tight frames 总被引:1,自引:0,他引:1
We show that every Bessel sequence (and therefore every frame) in a separable Hilbert space can be expanded to a tight frame by adding some elements. The proof is based on a recent generalization of the frame concept, the g-frame, which illustrates that g-frames could be useful in the study of frame theory. As an application, we prove that any Gabor frame can be expanded to a tight frame by adding one window function. 相似文献
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对于给定冗余的仿射框架X(Ф)={Ф1,…,ФL),存在对偶Y(ψ)={ψ1,…,ψL),这个对偶可能不是仿射框架,因为它不满足Bessel条件.这样的对偶我们称为伪仿射对偶,并给出伪仿射对偶框架的一种构造公式. 相似文献
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Banach空间中的X_d框架与Reisz基 总被引:1,自引:0,他引:1
本文引入并研究了Banach空间中的X_d框架,X_d Bessel列,紧X_d框架,独立X_d框架和X_d Riesz基等概念,给出了X_d框架和独立X_d框架的算子等价刻画,Banach空间X中存在X_d框架或X_d Riesz基的充要条件以及X_d框架的对偶框架存在的充要条件,讨论了Banach空间的基和X_d框架,X_d Riesz基之间的关系. 相似文献
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rpd Baricz 《Expositiones Mathematicae》2008,26(3):279-293
In this paper, we extend some known elementary trigonometric inequalities, and their hyperbolic analogues to Bessel and modified Bessel functions of the first kind. In order to prove our main results, we present some monotonicity and convexity properties of some functions involving Bessel and modified Bessel functions of the first kind. We also deduce some Turán and Lazarević-type inequalities for the confluent hypergeometric functions. 相似文献
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In this paper, we study the Dini functions and the cross-product of Bessel functions. Moreover, we are interested on the monotonicity patterns for the cross-product of Bessel and modified Bessel functions. In addition, we deduce Redheffer-type inequalities, and the interlacing property of the zeros of Dini functions and the cross-product of Bessel and modified Bessel functions. Bounds for logarithmic derivatives of these functions are also derived. The key tools in our proofs are some recently developed infinite product representations for Dini functions and cross-product of Bessel functions. 相似文献