New Characterizations of Riesz-Type Frames and Stability of Alternate Duals of Continuous Frames

Xiang, Zhong-Qi

doi:10.1155/2013/298982

Cited by 4 publications

(3 citation statements)

References 29 publications

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“…In this section by generalizing some results of [12], we get some equivalet conditions for Riesz-type continuous g-frames.…”

Section: Some Results Related To Riesz-type Continuous G-framesmentioning

confidence: 88%

Disjointness of continuous g-frames and Riesz-type continuous g-frames

Khedmati,

Abdollahpour

2018

Preprint

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In this paper we introduce concepts of disjoint, strongly disjoint and weakly disjoint continuous g-frames in Hilbert spaces and we get some equivalent conditions to these notions. We also construct a continuous g-frame by disjoint continuous g-frames. Furthermore, we provide some results related to the Riesz-type continuous g-frames.Definition 1.1. Let F = {f i } i∈I and G = {g i } i∈I be frames for Hilbert spaces H and K, respectively. We say that F and G are (i) Disjoint, if {f i ⊕ g i } i∈I is a frame for H ⊕ K.

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“…In this section by generalizing some results of [12], we get some equivalet conditions for Riesz-type continuous g-frames.…”

Section: Some Results Related To Riesz-type Continuous G-framesmentioning

confidence: 88%

Disjointness of continuous g-frames and Riesz-type continuous g-frames

Khedmati,

Abdollahpour

2018

Preprint

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“…It was shown in [17] that the difference between each arbitrary dual and the canonical dual of a continuous frame in Hilbert spaces can be considered as a bounded operator. In the following, we generalize it for Hilbert C * -modules.…”

Section: Construction Of Dual Continuous Framesmentioning

confidence: 99%

Continuous Riesz bases in Hilbert C*-modules

Ghasemi

Shateri

2023

Preprint

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“…There has recently been some interest in the study of (continuous) Riesz families [2,36], also called Riesz-type frames in [18]. Example 1(b) is a concrete version of [2,Proposition 3.7].…”

Section: Frame Theorymentioning

confidence: 99%

Density and duality theorems for regular Gabor frames

Jakobsen

Lemvig

2016

Journal of Functional Analysis

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We investigate Gabor frames on locally compact abelian groups with time-frequency shifts along non-separable, closed subgroups of the phase space. Density theorems in Gabor analysis state necessary conditions for a Gabor system to be a frame or a Riesz basis, formulated only in terms of the index subgroup. In the classical results the subgroup is assumed to be discrete. We prove density theorems for general closed subgroups of the phase space, where the necessary conditions are given in terms of the "size" of the subgroup. From these density results we are able to extend the classical Wexler-Raz biorthogonal relations and the duality principle in Gabor analysis to Gabor systems with time-frequency shifts along non-separable, closed subgroups of the phase space. Even in the euclidean setting, our results are new.

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New Characterizations of Riesz-Type Frames and Stability of Alternate Duals of Continuous Frames

Cited by 4 publications

References 29 publications

Disjointness of continuous g-frames and Riesz-type continuous g-frames

Disjointness of continuous g-frames and Riesz-type continuous g-frames

Continuous Riesz bases in Hilbert C*-modules

Density and duality theorems for regular Gabor frames

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