Maximal distributional chaos of weighted shift operators on Köthe sequence spaces

Xinxing Wu

Displaying similar documents to “Maximal distributional chaos of weighted shift operators on Köthe sequence spaces”

On the non-commutative neutrix product $ln x_{+} \circ x_{+}^{- s}$

Brian Fisher, Adem Kiliçman, Blagovest Damyanov, J. C. Ault (1996)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The non-commutative neutrix product of the distributions $ln x_{+}$ and $x_{+}^{- s}$ is proved to exist for $s = 1, 2, ...$ and is evaluated for $s = 1, 2$ . The existence of the non-commutative neutrix product of the distributions $x_{+}^{- r}$ and $x_{+}^{- s}$ is then deduced for $r, s = 1, 2, ...$ and evaluated for $r = s = 1$ .

On approximation of functions by certain operators preserving $x^{2}$

Lucyna Rempulska, Karolina Tomczak (2008)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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

Similarity:

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) $M_{S} (g) \in L ¹ (E)$ for any measurable set E of finite measure.

Defining complete and observable chaos

Víctor Jiménez López (1996)

Annales Polonici Mathematici

Similarity:

For a continuous map f from a real compact interval I into itself, we consider the set C(f) of points (x,y) ∈ I² for which $l i m i n f_{n \to \infty} | f^{n} (x) - f^{n} (y) | = 0$ and $l i m s u p_{n \to \infty} | f^{n} (x) - f^{n} (y) | > 0$ . We prove that if C(f) has full Lebesgue measure then it is residual, but the converse may not hold. Also, if λ² denotes the Lebesgue measure on the square and Ch(f) is the set of points (x,y) ∈ C(f) for which neither x nor y are asymptotically periodic, we show that λ²(C(f)) > 0 need not imply λ²(Ch(f)) > 0. We use these results to propose some plausible...

Topological size of scrambled sets

François Blanchard, Wen Huang, L'ubomír Snoha (2008)

Colloquium Mathematicae

Similarity:

A subset S of a topological dynamical system (X,f) containing at least two points is called a scrambled set if for any x,y ∈ S with x ≠ y one has $l i m i n f_{n \to \infty} d (f ⁿ (x), f ⁿ (y)) = 0$ and $l i m s u p_{n \to \infty} d (f ⁿ (x), f ⁿ (y)) > 0$ , d being the metric on X. The system (X,f) is called Li-Yorke chaotic if it has an uncountable scrambled set. These notions were developed in the context of interval maps, in which the existence of a two-point scrambled set implies Li-Yorke chaos and many other chaotic properties. In the present paper we address several questions about...

Displaying similar documents to “Maximal distributional chaos of weighted shift operators on Köthe sequence spaces”

On the non-commutative neutrix product ln x + ∘ x + - s

On approximation of functions by certain operators preserving x 2

A note on the strong maximal operator on ℝⁿ

Defining complete and observable chaos

Topological size of scrambled sets

On the non-commutative neutrix product $ln x_{+} \circ x_{+}^{- s}$

On approximation of functions by certain operators preserving $x^{2}$