Uncertainty principles associated to non-degenerate quadratic forms

Demange, Bruno

doi:10.24033/msmf.431

Cited by 12 publications

(16 citation statements)

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“…In the general case the conjecture is still open. In [2], Bruno Demange has also looked at the same question. There he could also prove a somewhat different characterisation for functions of one variable only and conjectures the analogue of his result in higher dimension.…”

Section: Remark 48mentioning

confidence: 92%

On the structure of analytic vectors for the Schrödinger representation

Garg

Thangavelu

2011

Monatsh Math

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Section: Remark 48mentioning

confidence: 92%

On the structure of analytic vectors for the Schrödinger representation

Garg

Thangavelu

2011

Monatsh Math

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“…This theorem has been further generalized where the pointwise condition (1) is replaced by integral conditions in [3], and by distributional conditions in [9]. Also see [13] and [15].…”

Section: Introductionmentioning

confidence: 93%

“…In the case ab < 1, the class of functions satisfying the condition (1) has been fully described by B. Demange [9]. In particular, it is an infinite-dimensional subset of L 2 (R).…”

Section: Introductionmentioning

confidence: 99%

Uncertainty principles for orthonormal sequences

Jaming

Powell

2007

Journal of Functional Analysis

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The aim of this paper is to provide complementary quantitative extensions of two results of H.S. Shapiro on the time-frequency concentration of orthonormal sequences in $L^2 (\R)$. More precisely, Shapiro proved that if the elements of an orthonormal sequence and their Fourier transforms are all pointwise bounded by a fixed function in $L^2(\R)$ then the sequence is finite. In a related result, Shapiro also proved that if the elements of an orthonormal sequence and their Fourier transforms have uniformly bounded means and dispersions then the sequence is finite. This paper gives quantitative bounds on the size of the finite orthonormal sequences in Shapiro's uncertainty principles. The bounds are obtained by using prolate sphero\"{i}dal wave functions and combinatorial estimates on the number of elements in a spherical code. Extensions for Riesz bases and different measures of time-frequency concentration are also given

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“…In view of this it is natural to ask for a characterisation of all functions f satisfying K a (f ) < ∞ for a fixed 0 < a < 1. An analogue of this problem in the context of Hardy's theorem has been studied by Demange [2], Vemuri [10] and the authors [5]. Recall the statement of Hardy's theorem [3]: If |f (x)| ≤ Ce −a|x| 2 , |f (y)| ≤ Ce −b|y| 2 then (i) f = 0 when ab > 1 4 , (ii) f (x) = Ce −a|x| 2 when ab = 1 4 and (iii) when ab < 1 4 there are infinitely many linearly independent functions (e.g.…”

Section: Introductionmentioning

confidence: 99%