The Hausdorff entropic moment problem

Romera, E.; Angulo, J. C.; Dehesa, J. S.

doi:10.1063/1.1360711

Cited by 27 publications

(27 citation statements)

References 19 publications

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“…The authors of [9] realize that other density reconstruction procedures, alternative to ordinary moments, would be desirable. We propose fractional moments density reconstruction procedure.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…This example is borrowed from [9]. Here the authors attempt to recover a nonnegative decreasing differentiable function f (x) from the frequency moments ω n , with…”

Section: Numerical Resultsmentioning

confidence: 99%

“…with H[f ] ≃ −0.06118227 (f (x), compared to [9], contains the normalizing constant 2). From f (x) we have ordinary moments µ n through a numerical procedure.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Functions f (x) and f M (x), obtained by 4 fractional moments, are practically indistinguishable. As a consequence, we argue that the use of 4 fractional moments is as effective as that of 8 frequency moments (as in [9]). The former ones, indeed, provide an approximant f M (x) practically indistinguishable from f (x) (see figure 1 of [9]).…”

Section: Inspection Ofmentioning

confidence: 99%

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Hausdorff moment problem via fractional moments

Inverardi

Pontuale

Petri

et al. 2003

Applied Mathematics and Computation

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We outline an efficient method for the reconstruction of a probability density function from the knowledge of its infinite sequence of ordinary moments. The approximate density is obtained resorting to maximum entropy technique, under the constraint of some fractional moments. The latter ones are obtained explicitly in terms of the infinite sequence of given ordinary moments. It is proved that the approximate density converges in entropy to the underlying density, so that it demonstrates to be useful for calculating expected values.

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Section: Numerical Resultsmentioning

confidence: 99%

“…This example is borrowed from [9]. Here the authors attempt to recover a nonnegative decreasing differentiable function f (x) from the frequency moments ω n , with…”

Section: Numerical Resultsmentioning

confidence: 99%

“…with H[f ] ≃ −0.06118227 (f (x), compared to [9], contains the normalizing constant 2). From f (x) we have ordinary moments µ n through a numerical procedure.…”

Section: Numerical Resultsmentioning

confidence: 99%

Section: Inspection Ofmentioning

confidence: 99%

See 2 more Smart Citations

Hausdorff moment problem via fractional moments

Inverardi

Pontuale

Petri

et al. 2003

Applied Mathematics and Computation

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“…for the Crámer-Rao [36][37][38], Fisher-Shannon [39,40] and LMC complexities [41], respectively. Each of them grasps the combined balance of two different facets of the probability density.…”

Section: Information-theoretic Measures: Basicsmentioning

confidence: 99%

Entropy and complexity properties of the d-dimensional blackbody radiation

Toranzo

Dehesa

2014

Eur. Phys. J. D

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Space dimensionality is a crucial variable in the analysis of the structure and dynamics of natural systems and phenomena. The dimensionality effects of the blackbody radiation has been the subject of considerable research activity in recent years. These studies are still somewhat fragmentary, posing formidable qualitative and quantitative problems for various scientific and technological areas. In this work we carry out an information-theoretical analysis of the spectral energy density of a d-dimensional blackbody at temperature T by means of various entropy-like quantities (disequilibrium, Shannon entropy, Fisher information) as well as by three (dimensionless) complexity measures (Crámer-Rao, Fisher-Shannon and LMC). All these frequency-functional quantities are calculated and discussed in terms of temperature and dimensionality. It is shown that all three measures of complexity have an universal character in the sense that they depend neither on temperature nor on the Planck and Boltzmann constants, but only on the the space dimensionality d. Moreover, they decrease when d is increasing; in particular, the values 2.28415, 1.90979 and 1.17685 are found for the Crámer-Rao, Fisher-Shannon and LMC measures of complexity of the 3-dimensional blackbody radiation, respectively. In addition, beyond the frequency at which the spectral density is maximum (which follows the well-known Wien displacement law), three further characteristic frequencies are defined in terms of the previous entropy quantities; they are shown to obey Wien-like laws. The potential usefulness of these distinctive features of the blackbody spectrum is physically discussed.

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Entropic functionals of Laguerre polynomials and complexity properties of the half‐line Coulomb potential

Sánchez-Moreno

Omiste

Dehesa

2011

Int J of Quantum Chemistry

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ABSTRACT:The stationary states of the half-line Coulomb potential are described by quantum-mechanical wavefunctions, which are controlled by the Laguerre polynomials L (1) n (x). Here, we first calculate the qth-order frequency or entropic moments of this quantum system, which is controlled by some entropic functionals of the Laguerre polynomials. These functionals are shown to be equal to a Lauricella function F, 1) by use of the Srivastava-Niukkanen linearization relation of Laguerre polynomials. The resulting general expressions are applied to obtain the following information-theoretic quantities of the half-line Coulomb potential: disequilibrium, Renyi and Tsallis entropies. An alternative and simpler expression for the linear entropy is also found by means of a different method. Then, the Shannon entropy and the LMC shape complexity of the lowest and highest (Rydberg) energetic states are explicitly given; moreover, sharp information-theoretic-based upper bounds to these quantities are found for general physical states. These quantities are numerically discussed for the ground and various excited states. Finally, the uncertainty measures of the half-line Coulomb potential given by the information-theoretic lengths are discussed.

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The Hausdorff entropic moment problem

Cited by 27 publications

References 19 publications

Hausdorff moment problem via fractional moments

Hausdorff moment problem via fractional moments

Entropy and complexity properties of the d-dimensional blackbody radiation

Entropic functionals of Laguerre polynomials and complexity properties of the half‐line Coulomb potential

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