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1.
Peter G. Casazza Gitta Kutyniok Mark C. Lammers 《Journal of Fourier Analysis and Applications》2004,10(4):383-408
Duality principles in Gabor theory such as the Ron–Shen duality principle and the
Wexler–Raz biorthogonality relations play a fundamental role for analyzing Gabor systems. In this
article we present a general approach to derive duality principles in abstract frame theory. For
each sequence in a separable Hilbert space we define a corresponding sequence dependent only
on two orthonormal bases. Then we characterize exactly properties of the first sequence in terms
of the associated one, which yields duality relations for the abstract frame setting. In the last part
we apply our results to Gabor systems. 相似文献
2.
P. G. Casazza C. L. Garcí a W. B. Johnson 《Proceedings of the American Mathematical Society》2001,129(10):3017-3023
Following Davie's example of a Banach space failing the approximation property (1973), we show how to construct a Banach space which is asymptotically Hilbertian and fails the approximation property. Moreover, the space is shown to be a subspace of a space with an unconditional basis which is ``almost' a weak Hilbert space and which can be written as the direct sum of two subspaces all of whose subspaces have the approximation property.
3.
4.
Peter G. Casazza Ole Christensen 《Proceedings of the American Mathematical Society》2001,129(1):145-154
A Weyl-Heisenberg frame
for allows every function to be written as an infinite linear combination of translated and modulated versions of the fixed function . In the present paper we find sufficient conditions for to be a frame for , which, in general, might just be a subspace of . Even our condition for to be a frame for is significantly weaker than the previous known conditions. The results also shed new light on the classical results concerning frames for , showing for instance that the condition A>0$">is not necessary for to be a frame for . Our work is inspired by a recent paper by Benedetto and Li, where the relationship between the zero-set of the function and frame properties of the set of functions is analyzed.
for allows every function to be written as an infinite linear combination of translated and modulated versions of the fixed function . In the present paper we find sufficient conditions for to be a frame for , which, in general, might just be a subspace of . Even our condition for to be a frame for is significantly weaker than the previous known conditions. The results also shed new light on the classical results concerning frames for , showing for instance that the condition A>0$">is not necessary for to be a frame for . Our work is inspired by a recent paper by Benedetto and Li, where the relationship between the zero-set of the function and frame properties of the set of functions is analyzed.
5.
6.
AA Yan LI Kai CAO ZhongHua & HU WenRui Key Laboratory of Microgravity 《中国科学:物理学 力学 天文学(英文版)》2011,(2)
The dependency of the critical Marangoni number on the geometrical aspect ratio of the floating half zone is essential to predict the onset of oscillatory thermocapillary convection.The experimental studies in the microgravity conditions on floating half zones of several centimeters in diameter have predicted that the critical Marangoni number increases with the increasing aspect ratio,and the terrestrial experimental studies have predicted the contradictory conclusion for floating half zones of several mil... 相似文献
7.
Non-Gravitational Effects with Density-Matching in Evaluating the Influence of Sedimentation on Colloidal Coagulation 下载免费PDF全文
The method of density matching between the solid and liquid phases is often adopted to effectively eliminate the effect of sedimentation of suspensions in studies on dynamic behaviour of a colloidal system. However, the associated changes in the solvent composition may bring side effects to the properties investigated and therefore might lead to a faulty conclusion if the relevant correction is not made. To illustrate the importance of this side effect, we present an example of the sedimentation influence on the coagulation rate of suspensions of 2μm (diameter) polystyrene. The liquid mixtures, in the proper proportions of water (H2O), deuterium oxide (D2O) and methanol (MeOH) as the liquid phase, density-matched and unmatched experiments are performed. Besides the influence of viscosity, the presence of methanol in solvent media, used to enhance the sedimentation effect, causes significant changes (reduction) in rapid coagulation rates compared to that in pure water. Without the relevant corrections for those non-gravitational factors it seems that gravitational sedimentation would retard the coagulation. The magnitude of the contribution from the non-gravitational factor is quantitatively determined, making the relevant correction possible. After necessary the influence of the sedimentation on coagulation rates at corrections for all factors, our experiments show that the initial stage of the coagulation is not observable. 相似文献
8.
9.
Frame expansions in separable Banach spaces 总被引:2,自引:0,他引:2
Banach frames are defined by straightforward generalization of (Hilbert space) frames. We characterize Banach frames (and Xd-frames) in separable Banach spaces, and relate them to series expansions in Banach spaces. In particular, our results show that we can not expect Banach frames to share all the nice properties of frames in Hilbert spaces. 相似文献
10.