Generalized Sampling in $${L}^{2}({\mathbb{R}}^{d})$$ Shift-Invariant Subspaces with Multiple Stable Generators

On Regular Generalized Sampling in T-Invariant Subspaces of a Hilbert Space: An Overview

Numerical Functional Analysis and Optimization ◽

10.1080/01630563.2019.1667827 ◽

2019 ◽

Vol 41 (6) ◽

pp. 685-709

Author(s):

Antonio G. García ◽

María J. Muñoz-Bouzo ◽

Gerardo Pérez-Villalón

Keyword(s):

Hilbert Space ◽

Invariant Subspaces ◽

Generalized Sampling

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Generalized sampling: From shift-invariant to U-invariant spaces

Analysis and Applications ◽

10.1142/s0219530514500213 ◽

2015 ◽

Vol 13 (03) ◽

pp. 303-329 ◽

Cited By ~ 10

Author(s):

H. R. Fernández-Morales ◽

A. G. García ◽

M. A. Hernández-Medina ◽

M. J. Muñoz-Bouzo

Keyword(s):

Invariant Subspaces ◽

Invertible Operator ◽

Continuous Group ◽

Sampling Frame ◽

Generalize Convolution ◽

Time Jitter ◽

Generalized Sampling ◽

Frame Expansions ◽

Invariant Spaces ◽

Convolution Systems

The aim of this article is to derive a sampling theory in U-invariant subspaces of a separable Hilbert space ℋ where U denotes a unitary operator defined on ℋ. To this end, we use some special dual frames for L2(0, 1), and the fact that any U-invariant subspace with stable generator is the image of L2(0, 1) by means of a bounded invertible operator. The used mathematical technique mimics some previous sampling work for shift-invariant subspaces of L2(ℝ). Thus, sampling frame expansions in U-invariant spaces are obtained. In order to generalize convolution systems and deal with the time-jitter error in this new setting we consider a continuous group of unitary operators which includes the operator U.

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On Generalizations of Sampling Theorem and Stability Theorem in Shift-Invariant Subspaces of Lebesgue and Wiener Amalgam Spaces with Mixed-Norms

Symmetry ◽

10.3390/sym13020331 ◽

2021 ◽

Vol 13 (2) ◽

pp. 331

Author(s):

Junjian Zhao ◽

Marko Kostić ◽

Wei-Shih Du

Keyword(s):

Invariant Subspaces ◽

Sampling Theorem ◽

Stability Theorem ◽

Wiener Amalgam Spaces ◽

Mixed Norms ◽

Sampling Theorems ◽

Generalized Sampling ◽

Stability Theorems ◽

Amalgam Spaces ◽

New Inequalities

In this paper, we establish generalized sampling theorems, generalized stability theorems and new inequalities in the setting of shift-invariant subspaces of Lebesgue and Wiener amalgam spaces with mixed-norms. A convergence theorem of general iteration algorithms for sampling in some shift-invariant subspaces of Lp→(Rd) are also given.

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Invariant Subspaces on KPC-Hypergroups

Zurnal matematiceskoj fiziki analiza geometrii ◽

10.15407/mag15.01.122 ◽

2019 ◽

Vol 15 (1) ◽

pp. 122-130

Author(s):

Laszlo Szekelyhidi ◽

◽

Seyyed Mohammad Tabatabaie ◽

Keyword(s):

Invariant Subspaces

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On Hamiltonian Matrices, Symplectic Transformations, and Invariant Subspaces

1993 American Control Conference ◽

10.23919/acc.1993.4793136 ◽

1993 ◽

Author(s):

R.V. Patel

Keyword(s):

Invariant Subspaces

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FORMULATION AND SOLUTION OF OPTIMIZATION PROBLEM REDUNDANCY SYSTEM COMPRISING SITUATION CENTER

Informatization and communication ◽

10.34219/2078-8320-2019-10-3-44-50 ◽

2019 ◽

pp. 44-50

Author(s):

A.V. Alekseev

Keyword(s):

Analytical Model ◽

Quality Indicators ◽

Significant Influence ◽

Optimization Problem ◽

Sampling Theorem ◽

Sampling Frequency ◽

Generalized Sampling ◽

Optimal Value ◽

Situation Center ◽

Situation Centers

The analysis of the concept, properties and features of heterogeneous redundancy in modern complex ergatic systems, including those included in the situation centers (SC). On the basis of the qualimetric paradigm, the generalized analytical model of quality and optimization of quality by private, group, summary and aggregated quality indicators is justified. Practical ways of realization of the model and methods of optimization of the objects which are a part of SC and them as a whole at the expense of reduction of structural, functional and other types of redundancy under the obligatory condition of non-reduction of the required value of quality are given. On the example of the generalized sampling theorem when choosing the optimal value of the sampling frequency of the real bandpass signal, the criticality and significant influence on the redundancy of data in their further processing in the SC is shown.

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