Coherent state transforms attached to generalized Bargmann spaces on the complex plane

Mouayn, Zouhaïr

doi:10.1002/mana.200910191

Cited by 24 publications

(20 citation statements)

References 12 publications

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“…Summarizing the above calculations and taking into account the previous prefactors, we arrive at the announced result (24).…”

Section: Proof Of Propositionmentioning

confidence: 68%

“…Note that when m = 0, h 0 j (z) reduces to h j (z) in (3). Therefore, we may replace the coefficients h j (z) by h m j (z) to construct a family of coherent states depending on the parameter m. This leads to the coherent states transform B m : L 2 (R) → A m (C), defined for any f ∈ L 2 (R) by [24]:…”

Section: Introduction and Statement Of The Resultsmentioning

confidence: 99%

“…In particular, for z = w in ( 24), the condition 〈Ψ z,m,q , Ψ z,m,q 〉 L 2 (R) = 1 may provide us with the normalization factor (20). Furthermore, (24) gives an explicit expression for the function…”

Section: Introduction and Statement Of The Resultsmentioning

confidence: 99%

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A q-deformation of true-polyanalytic Bargmann transforms when q -1 >1

Moize¹,

Mouayn²

2022

Comptes Rendus. Mathématique

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We combine continuous q −1 -Hermite Askey polynomials with new 2D orthogonal polynomials introduced by Ismail and Zhang as q-analogs for complex Hermite polynomials to construct a new set of coherent states depending on a nonnegative integer parameter m. Our construction leads to a new qdeformation of the m-true-polyanalytic Bargmann transform on the complex plane. In the analytic case m = 0, the obtained coherent states transform can be associated with the Arïk-Coon oscillator for q = q −1 > 1. These result may be used to introduce a q-deformed Ginibre-type point process.

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“…Summarizing the above calculations and taking into account the previous prefactors, we arrive at the announced result (24).…”

Section: Proof Of Propositionmentioning

confidence: 68%

Section: Introduction and Statement Of The Resultsmentioning

confidence: 99%

See 1 more Smart Citation

A q-deformation of true-polyanalytic Bargmann transforms when q -1 >1

Moize¹,

Mouayn²

2022

Comptes Rendus. Mathématique

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“…Balk ([11]). The lines of current research on polyanalytic functions are various : the problem of the best uniform approximation by N −analytic polynomials ( [30]- [32], [51]), the study of wavelets and Gabor frames ([2]- [5], [9]), the timefrequency analysis ( [5], [7], [8]), the sampling and interpolation in function spaces ( [1]), the study of coherent states in quantum mechanics ( [19], [36]), [37]), the image and signal processing ( [6], [7]), etc. Gevrey classes, which are also, but in a completely different way, a generalisation of real analytic functions, were first introduced by Gevrey ( [16]).…”

Section: Introductionmentioning

confidence: 99%

On the Representation and the Uniform Polynomial Approximation of Polyanalytic Functions of Gevrey Type on the Unit Disk

Kabbaj

Zoubeir

2021

IJMSI

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In this paper we define Gevrey polyanalytic classes of order N on the unit disk D and we obtain for these classes a characteristic expansion into N −analytic polynomials on suitable neighborhoods of D. As an application of our main theorem, we perform for the Gevrey polyanalytic classes of order N on the unit disk D, an analogue to E. M. Dyn'kin's theorem. We also derive, for these classes, their characteristic degree of the best uniform approximation on D by N −analytic polynomials.

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“…Our procedure can be described as follows. In [5] we have introduced a family of CS for the HO potential through superpositions of the corresponding eigenstates where the role of coefficients z n / √ n! of the canonical CS was played by coefficients where L (α) n (.)…”

Section: Introductionmentioning

confidence: 99%

Epsilon coherent states with polyanalytic coefficients for the harmonic oscillator

Mouayn

2017

Anal.Math.Phys.

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We construct a new class of coherent states indexed by points z of the complex plane and depending on two positive parameters m and ε > 0 by replacing the coefficients z n / √ n! of the canonical coherent states by polyanalytic functions. These states solve the identity of the states Hilbert space of the harmonic oscillator at the limit ε → 0 + and obey a thermal stability property. Their wavefunctions are obtained in a closed form and their associated Bargmann-type transform is also discussed.

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Coherent state transforms attached to generalized Bargmann spaces on the complex plane

Cited by 24 publications

References 12 publications

A q-deformation of true-polyanalytic Bargmann transforms when q -1 >1

A q-deformation of true-polyanalytic Bargmann transforms when q -1 >1

On the Representation and the Uniform Polynomial Approximation of Polyanalytic Functions of Gevrey Type on the Unit Disk

Epsilon coherent states with polyanalytic coefficients for the harmonic oscillator

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