Displaying similar documents to “On the non-commutative neutrix product ln x + ∘ x + - s ”

On approximation of functions by certain operators preserving x 2

Lucyna Rempulska, Karolina Tomczak (2008)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we extend the Duman-King idea of approximation of functions by positive linear operators preserving e k ( x ) = x k , k = 0 , 2 . Using a modification of certain operators L n preserving e 0 and e 1 , we introduce operators L n * which preserve e 0 and e 2 and next we define operators L n ; r * for r -times differentiable functions. We show that L n * and L n ; r * have better approximation properties than L n and L n ; r .

A note on the strong maximal operator on ℝⁿ

Jiecheng Chen, Xiangrong Zhu (2004)

Studia Mathematica

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We prove that for f ∈ L ln⁺L(ℝⁿ) with compact support, there is a g ∈ L ln⁺L(ℝⁿ) such that (a) g and f are equidistributed, (b) M S ( g ) ∈ L ¹ ( E ) for any measurable set E of finite measure.

Maximal distributional chaos of weighted shift operators on Köthe sequence spaces

Xinxing Wu (2014)

Czechoslovak Mathematical Journal

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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...