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AN UNCERTAINTY PRINCIPLE FOR A MODIFIED
"... ABSTRACT. An uncertainty principle is obtained for a modified Yνtransform of order ν. The principle is similar to the classical HeisenbergWeyl uncertainty principle for the Fourier transform on R. ..."
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ABSTRACT. An uncertainty principle is obtained for a modified Yνtransform of order ν. The principle is similar to the classical HeisenbergWeyl uncertainty principle for the Fourier transform on R.
Three uncertainty principles for an abelian locally compact group. Lectures given at the workshop ”Representation Theory of Lie Groups
, 2003
"... The purpose of this article is to direct reader’s attention to some recent developments concerning three Uncertainty Principles: the classical HeisenbergWeyl Uncertainty Principle, The HirschmanBeckner Uncertainty Principle based on the notion of the entropy, and the DonohoStark Uncertainty Prin ..."
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Cited by 2 (0 self)
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The purpose of this article is to direct reader’s attention to some recent developments concerning three Uncertainty Principles: the classical HeisenbergWeyl Uncertainty Principle, The HirschmanBeckner Uncertainty Principle based on the notion of the entropy, and the DonohoStark Uncertainty
On the HeisenbergWeyl inequality
 J. Inequ. Pure & Appl. Math
, 2005
"... ABSTRACT. The wellknown second order moment HeisenbergWeyl inequality (or uncertainty relation) in Fourier Analysis states: Assume that f: R → C is a complex valued function of a random real variable x such that f ∈ L2 (R). Then the product of the second moment of the random real x for f  2 and ..."
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Cited by 9 (3 self)
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ABSTRACT. The wellknown second order moment HeisenbergWeyl inequality (or uncertainty relation) in Fourier Analysis states: Assume that f: R → C is a complex valued function of a random real variable x such that f ∈ L2 (R). Then the product of the second moment of the random real x for f  2
An uncertainty principle for the Dunkl transform
"... This note presents an analogue of the classical HeisenbergWeyl uncertainty principle for the Dunkl transform on R N : Its proof is based on expansions with respect to generalized Hermite functions. 1991 AMS Subject Classification: Primary: 33C80; 43A32. Secondary: 42C15, 26D10 1 Introduction The ..."
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Cited by 11 (0 self)
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This note presents an analogue of the classical HeisenbergWeyl uncertainty principle for the Dunkl transform on R N : Its proof is based on expansions with respect to generalized Hermite functions. 1991 AMS Subject Classification: Primary: 33C80; 43A32. Secondary: 42C15, 26D10 1 Introduction
Extensions of the HeisenbergWeyl inequality
 MR 87i:26013 236
, 1986
"... ABSTRACT. In this paper a number of generalizations of the classical HeisenbergWeyl uncertainty inequality are given. We prove the ndimensional Hirschman entropy inequality (Theorem 2.1) from the optimal form of the HausdorffYoung theorem and deduce a higher dimensional uncertainty inequality (T ..."
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Cited by 3 (0 self)
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ABSTRACT. In this paper a number of generalizations of the classical HeisenbergWeyl uncertainty inequality are given. We prove the ndimensional Hirschman entropy inequality (Theorem 2.1) from the optimal form of the HausdorffYoung theorem and deduce a higher dimensional uncertainty inequality
On the refined HeisenbergWeyl type inequality
 J. Inequ. Pure & Appl. Math
, 2005
"... ABSTRACT. The wellknown second moment HeisenbergWeyl inequality (or uncertainty relation) states: Assume that f: R → C is a complex valued function of a random real variable x such that f ∈ L2 (R), where R = (−∞, ∞). Then the product of the second moment of the random real x for f  2 and the sec ..."
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Cited by 2 (2 self)
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ABSTRACT. The wellknown second moment HeisenbergWeyl inequality (or uncertainty relation) states: Assume that f: R → C is a complex valued function of a random real variable x such that f ∈ L2 (R), where R = (−∞, ∞). Then the product of the second moment of the random real x for f  2
Decoding by Linear Programming
, 2004
"... This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector f ∈ Rn from corrupted measurements y = Af + e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible to rec ..."
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Cited by 1399 (16 self)
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in this paper improve on our earlier work [5]. Finally, underlying the success of ℓ1 is a crucial property we call the uniform uncertainty principle that we shall describe in detail.
The quantum structure of spacetime at the Planck scale and quantum fields
 COMMUN. MATH. PHYS. 172, 187–220 (1995)
, 1995
"... We propose uncertainty relations for the different coordinates of spacetime events, motivated by Heisenberg’s principle and by Einstein’s theory of classical gravity. A model of Quantum Spacetime is then discussed where the commutation relations exactly implement our uncertainty relations. We outl ..."
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Cited by 332 (6 self)
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We propose uncertainty relations for the different coordinates of spacetime events, motivated by Heisenberg’s principle and by Einstein’s theory of classical gravity. A model of Quantum Spacetime is then discussed where the commutation relations exactly implement our uncertainty relations. We
An Uncertainty Principle For Hankel Transforms
"... There exists a generalized Hankel transform of order ff \Gamma1=2 on R, which is based on the eigenfunctions of the Dunkl operator T ff f(x) = f 0 (x) + \Gamma ff + 1 2 \Delta f(x) \Gamma f(\Gammax) x ; f 2 C 1 (R): For ff = \Gamma1=2 this transform coincides with the usual Fourier transf ..."
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Cited by 21 (4 self)
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transform on R. In this paper the operator T ff replaces the usual first derivative in order to obtain a sharp uncertainty principle for generalized Hankel transforms on R. It generalizes the classical WeylHeisenberg uncertainty principle for the position and momentum operators on L 2 (R); moreover
On the Uncertainty Principle in Harmonic Analysis
, 2000
"... The Uncertainty Principle (UP) as understood in this lecture is the following informal assertion: a nonzero “object” (a function, distribution, hyperfunction) and its Fourier image cannot be too small simultaneously. “The smallness” is understood in a very broad sense meaning fast decay (at infini ..."
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Cited by 97 (1 self)
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The Uncertainty Principle (UP) as understood in this lecture is the following informal assertion: a nonzero “object” (a function, distribution, hyperfunction) and its Fourier image cannot be too small simultaneously. “The smallness” is understood in a very broad sense meaning fast decay (at
Results 1  10
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358