Calderón type formula in Quantum calculus

Nemri, Akram; Selmi, Belgacem

doi:10.1016/j.indag.2013.02.004

Cited by 4 publications

(3 citation statements)

References 11 publications

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“…Calderón's reproducing formula was also established for Bessel operator [4,5]. This work is a continuation of a last work [9], and we establish formula for q-Bessel convolution for both functions and measures witch generalize the above one. In the classical case this formula is expressed for a suitable function f as follows:…”

Section: Introductionmentioning

confidence: 64%

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Calderóns reproducing Formula For q-Bessel operator

Selmi¹

2015

Cubo

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Section: Introductionmentioning

confidence: 64%

“…Definition 2.6. [11,9] A bounded complex even measure µ on R q is a bounded linear functional µ on H q, * (R q ), i.e., for all f in H q, * (R q ), we have…”

Section: 7mentioning

confidence: 99%

Calderóns reproducing Formula For q-Bessel operator

Selmi¹

2015

Cubo

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“…(1.8) is replaced by the number "1" and hence we get the well-known Jackson derivative in ref. [6][7][8][9] which is given by Eq. (1.9)…”

Section: Quantum Calculusmentioning

confidence: 99%

q-Calculus and the Symmetrized Radioactive Decay Law

Eastmond¹

2021

Preprint

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The radioactive decay law was first formulated by Ernest Rutherford and Frederick Soddy in 1902. As a well-known law, one of its primary applications is to determine the dates of ancient specimens. The process is known as radiocarbon dating and is subjected to the known properties of radioactive nuclei. In this paper, we implement quantum calculus to express the solution of the radioactive decay equation in symmetrized q-exponential form. Also, we explore a q-analog of the decay constant using Tsallis logarithmic function for various miscellaneous q-values. Furthermore, the factor-label method was applied to our analysis to show that the correct units remained intact under the application of quantum calculus. In conclusion, our work suggests that a variation of the q-parameter was akin to the production of a new isotope for all q in (0,1); the superadditive regime.

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Lipschitz and Besov spaces in quantum calculus

Nemri

Selmi

2016

Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

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The purpose of this paper is to investigate the harmonic analysis on the time scale [Formula: see text], [Formula: see text] to introduce [Formula: see text]-weighted Besov spaces subspaces of [Formula: see text] generalizing the classical one. Further, using an example of [Formula: see text]-weighted [Formula: see text] which is introduced and studied. We give a new characterization of the [Formula: see text]-Besov space using [Formula: see text]-Poisson kernel and the [Formula: see text] Littlewood–Paley operator.

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Calderón type formula in Quantum calculus

Cited by 4 publications

References 11 publications

Calderóns reproducing Formula For q-Bessel operator

Calderóns reproducing Formula For q-Bessel operator

q-Calculus and the Symmetrized Radioactive Decay Law

Lipschitz and Besov spaces in quantum calculus

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Calderón type formula in Quantum calculus

Cited by 4 publications

References 11 publications

Calderóns reproducing Formula For q-Bessel operator

Calderóns reproducing Formula For q-Bessel operator

q-Calculus and the Symmetrized Radioactive Decay Law

Lipschitz and Besov spaces in quantum calculus

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Resources

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Calderóns reproducing Formula For q-Bessel operator

Calderóns reproducing Formula For q-Bessel operator