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Keywords = Redheffer inequality

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17 pages, 329 KB  
Article
Redheffer-Type Bounds of Special Functions
by Reem Alzahrani and Saiful R. Mondal
Mathematics 2023, 11(2), 379; https://doi.org/10.3390/math11020379 - 11 Jan 2023
Cited by 1 | Viewed by 1835
Abstract
In this paper, we aim to construct inequalities of the Redheffer type for certain functions defined by the infinite product involving the zeroes of these functions. The key tools used in our proofs are classical results on the monotonicity of the ratio of [...] Read more.
In this paper, we aim to construct inequalities of the Redheffer type for certain functions defined by the infinite product involving the zeroes of these functions. The key tools used in our proofs are classical results on the monotonicity of the ratio of differentiable functions. The results are proved using the nth positive zero, denoted by bn(ν). Special cases lead to several examples involving special functions, namely, Bessel, Struve, and Hurwitz functions, as well as several other trigonometric functions. Full article
31 pages, 404 KB  
Review
Spherical-Symmetry and Spin Effects on the Uncertainty Measures of Multidimensional Quantum Systems with Central Potentials
by Jesús S. Dehesa
Entropy 2021, 23(5), 607; https://doi.org/10.3390/e23050607 - 14 May 2021
Cited by 9 | Viewed by 2515
Abstract
The spreading of the stationary states of the multidimensional single-particle systems with a central potential is quantified by means of Heisenberg-like measures (radial and logarithmic expectation values) and entropy-like quantities (Fisher, Shannon, Rényi) of position and momentum probability densities. Since the potential is [...] Read more.
The spreading of the stationary states of the multidimensional single-particle systems with a central potential is quantified by means of Heisenberg-like measures (radial and logarithmic expectation values) and entropy-like quantities (Fisher, Shannon, Rényi) of position and momentum probability densities. Since the potential is assumed to be analytically unknown, these dispersion and information-theoretical measures are given by means of inequality-type relations which are explicitly shown to depend on dimensionality and state’s angular hyperquantum numbers. The spherical-symmetry and spin effects on these spreading properties are obtained by use of various integral inequalities (Daubechies–Thakkar, Lieb–Thirring, Redheffer–Weyl, ...) and a variational approach based on the extremization of entropy-like measures. Emphasis is placed on the uncertainty relations, upon which the essential reason of the probabilistic theory of quantum systems relies. Full article
(This article belongs to the Special Issue Entropies, Divergences, Information, Identities and Inequalities)
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