Sobolev type spaces in quantum calculus

Nemri, Akram; Selmi, Belgacem

doi:10.1016/j.jmaa.2009.06.008

Cited by 6 publications

(5 citation statements)

References 9 publications

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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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“…(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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“…Let s ≥ 0 . We define the q -Sobolev space [18] of order s , that will be denoted H * , q s ( ℝ q ) , as the set of all f ∈ L 2 ( ℝ q , + ) such that ( 1 + z 2 ) s / 2 F q ( f ) ( z ) ∈ L 2 ( ℝ q , + ) . The space H * , q s ( ℝ q ) provided with the inner product…”

Section: Q-fourier Multiplier Operatorsmentioning

confidence: 99%

“…The Hilbert space H * , q s ( ℝ q ) satisfies (see [18, 19]) the following properties.…”

Section: Q-fourier Multiplier Operatorsmentioning

confidence: 99%

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Analytical approximation formulas in quantum calculus

Nemri

Soltani

2016

Mathematics and Mechanics of Solids

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We study the class of q-Fourier multiplier operators T m : = F q ( F q ) , which are acted on the q-Sobolev space H * , q s ( ℝ q ) , and we obtain the exact expression and some properties for the extremal functions of the best approximation problem in quantum calculus inf f ∈ H * , q s ( ℝ q ) { η ∥ f ∥ H * , q s ( ℝ q ) 2 + ∥ g − T m f ∥ L 2 ( ℝ q , + ) 2 } , where η > 0 and g ∈ L 2 ( ℝ q , + ) . As an application, we provide numerical approximate formulas for a limit case η ↑ 0 ; using q-calculus, which generalizes the Gauss-Kronrod method studied given in [14] in one-dimensional space.

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“…These spaces can be described by means of difference differential operator (see [14], [15], [18], [23]). Throughout the paper weight w : R q,+ −→ R + will be a q-measurable function, w > 0 a.e., and we will give a characterization of weighted q-Besov spaces.…”

Section: Introductionmentioning

confidence: 99%