Perturbation of frame sequences and its applications to shift-invariant spaces

Koo, Yoo Young; Lim, Jae Kun

doi:10.1016/j.laa.2006.07.009

Cited by 12 publications

(10 citation statements)

References 21 publications

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“…This problem is related to frame theory. However, even if the literature on this subject is huge (see for instance [16,4,9,11,12,8,5,23]), the results we needed did not seem to be available.…”

Section: Discussionmentioning

confidence: 99%

Averaged controllability of parameter dependent conservative semigroups

Lohéac

Zuazua

2017

Journal of Differential Equations

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International audienceWe consider the problem of averaged controllability for parameter depending (either in a discrete or continuous fashion) control systems, the aim being to find a control, independent of the unknown parameters, so that the average of the states is controlled. We do it in the context of conservative models, both in an abstract setting and also analysing the specific example of the wave equation. Our first result is of perturbative nature. Assuming the averaging probability measure to be a small parameter-dependent perturbation (in a sense that we make precise) of an atomic measure given by a Dirac mass corresponding to a specific realisation of the system, we show that the averaged controllability property is achieved whenever the system corresponding to the support of the Dirac is controllable. Similar tools can be employed to obtain averaged versions of the so-called Ingham inequalities. Particular attention is devoted to 1d wave and Schrödinger equations in which the time-periodicity of solutions can be exploited to obtain more precise results, provided the parameters involved satisfy Diophantine conditions ensuring the lack of resonances

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Section: Discussionmentioning

confidence: 99%

Averaged controllability of parameter dependent conservative semigroups

Lohéac

Zuazua

2017

Journal of Differential Equations

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“…The study of these type of factorizations as well as estimation for the norm of oblique projections are very useful to study different problems in modern harmonic analysis. For instance it has been used to study the biorthogonality of two multiresolution analyses , problems on perturbation of frames , and problems concerning sampling theory (see for example [16][17][18]8,[19][20][21]26,7,3,9] and the references cited therein).…”

Section: Motivation Of the Problemmentioning

confidence: 99%

Singular value estimates of oblique projections

Antezana

Corach

2009

Linear Algebra and its Applications

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“…10,12,17,28 However, the remaining parameters are rarely (if ever) used in applications of the perturbation theorems to wavelet, Gabor, shift-invariant, or exponential frames.…”

Section: 15 17mentioning

confidence: 99%