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Matrix-Variate Statistical Distributions and Fractional Calculus

Mathai, A., Haubold, H. (2011)

Fractional Calculus and Applied Analysis

MSC 2010: 15A15, 15A52, 33C60, 33E12, 44A20, 62E15 Dedicated to Professor R. Gorenflo on the occasion of his 80th birthdayA connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results on matrix-variate statistical densities and their connections to fractional calculus will be established. When considering solutions of fractional...

Maximal distributional chaos of weighted shift operators on Köthe sequence spaces

Xinxing Wu (2014)

Czechoslovak Mathematical Journal

During the last ten some years, many research works were devoted to the chaotic behavior of the weighted shift operator on the Köthe sequence space. In this note, a sufficient condition ensuring that the weighted shift operator B w n : λ p ( A ) → λ p ( A ) defined on the Köthe sequence space λ p ( A ) exhibits distributional ϵ -chaos for any 0 < ϵ < diam λ p ( A ) and any n ∈ ℕ is obtained. Under this assumption, the principal measure of B w n is equal to 1. In particular, every Devaney chaotic shift operator exhibits distributional ϵ -chaos for any 0 < ϵ < diam λ p ( A ) .

Maximal scrambled sets for simple chaotic functions.

Víctor Jiménez López (1996)

Publicacions Matemàtiques

This paper is a continuation of [1], where a explicit description of the scrambled sets of weakly unimodal functions of type 2∞ was given. Its aim is to show that, for an appropriate non-trivial subset of the above family of functions, this description can be made in a much more effective and informative way.

McShane equi-integrability and Vitali’s convergence theorem

Jaroslav Kurzweil, Štefan Schwabik (2004)

Mathematica Bohemica

The McShane integral of functions f I → ℝ defined on an m -dimensional interval I is considered in the paper. This integral is known to be equivalent to the Lebesgue integral for which the Vitali convergence theorem holds. For McShane integrable sequences of functions a convergence theorem based on the concept of equi-integrability is proved and it is shown that this theorem is equivalent to the Vitali convergence theorem.

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