arXiv 1102.32932011-02math.FA

On $Δ$-quasi-slowly oscillating sequences

Huseyin Cakalli

备注：: This paper has been withdrawn by the author due to the publication in the journal, Computer and Mathematics with Applications

英文摘要：

A sequence $(x_{n})$ of points in a topological group is called $Δ$-quasi-slowly oscillating if $(Δx_{n})$ is quasi-slowly oscillating, and is called quasi-slowly oscillating if $(Δx_{n})$ is slowly oscillating. A function $f$ defined on a subset of a topological group is quasi-slowly (respectively, $Δ$-quasi-slowly) oscillating continuous if it preserves quasi-slowly (respectively, $Δ$-quasi-slowly) oscillating sequences, i.e. $(f(x_{n}))$ is quasi-slowly (respectively, $Δ$-quasi-slowly) oscillating whenever $(x_{n})$ is. We study these kinds of continuities, and investigate relations with statistical continuity, lacunary statistical continuity, and some other types of continuities in metrizable topological groups.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Calkin images of Fourier convolution operators with slowly oscillating symbols

Let $Φ$ be a $C^*$-subalgebra of $L^\infty(\mathbb{R})$ and $SO_{X(\mathbb{R})}^\diamond$ be the Banach algebra of slowly oscillating Fourier multipliers on a Banach function space $X(\mathbb{R})$. We show that the intersection of the Calkin image of the algebra generated by the operators of multiplication $aI$ by functions $a\inΦ$ and the Calkin image of the algebra generated by the Fourier convolution operators $W^0(b)$ with symbols in $SO_{X(\mathbb{R})}^\diamond$ coincides with the Calkin image of the algebra generated by the operators of multiplication by constants.

2020-08-04math.FA

Sufficient Conditions for Fredholmness of Singular Integral Operators with Shifts and Slowly Oscillating Data

Suppose $α$ is an orientation preserving diffeomorphism (shift) of $\mR_+=(0,\infty)$ onto itself with the only fixed points $0$ and $\infty$. We establish sufficient conditions for the Fredholmness of the singular integral operator \[ (aI-bW_α)P_++(cI-dW_α)P_- \] acting on $L^p(\mR_+)$ with $1<p<\infty$, where $P_\pm=(I\pm S)/2$, $S$ is the Cauchy singular integral operator, and $W_αf=f\circα$ is the shift operator, under the assumptions that the coefficients $a,b,c,d$ and the derivative $α'$ of the shift are bounded and continuous on $\mR_+$ and may admit discontinuities of slowly oscillatin…

2010-09-28math.FA

Necessary Conditions for Fredholmness of Singular Integral Operators with Shifts and Slowly Oscillating Data

Suppose $α$ is an orientation-preserving diffeomorphism (shift) of $\mR_+=(0,\infty)$ onto itself with the only fixed points $0$ and $\infty$. In \cite{KKLsufficiency} we found sufficient conditions for the Fredholmness of the singular integral operator with shift \[ (aI-bW_α)P_++(cI-dW_α)P_- \] acting on $L^p(\mR_+)$ with $1<p<\infty$, where $P_\pm=(I\pm S)/2$, $S$ is the Cauchy singular integral operator, and $W_αf=f\circα$ is the shift operator, under the assumptions that the coefficients $a,b,c,d$ and the derivative $α'$ of the shift are bounded and continuous on $\mR_+$ and may admit disc…

2010-10-26math.FA

On a Weighted Singular Integral Operator with Shifts and Slowly Oscillating Data

Let $α,β$ be orientation-preserving diffeomorphism (shifts) of $\mathbb{R}_+=(0,\infty)$ onto itself with the only fixed points $0$ and $\infty$ and $U_α,U_β$ be the isometric shift operators on $L^p(\mathbb{R}_+)$ given by $U_αf=(α')^{1/p}(f\circα)$, $U_βf=(β')^{1/p}(f\circβ)$, and $P_2^\pm=(I\pm S_2)/2$ where \[ (S_2 f)(t):=\frac{1}{πi}\int\limits_0^\infty \left(\frac{t}τ\right)^{1/2-1/p}\frac{f(τ)}{τ-t}\,dτ, \quad t\in\mathbb{R}_+, \] is the weighted Cauchy singular integral operator. We prove that if $α',β'$ and $c,d$ are continuous on $\mathbb{R}_+$ and slowly oscillating at $0$ and $\inf…

2015-01-15math.FA

Semi-Fredholmness of weighted singular integral operators with shifts and slowly oscillating data

Let $α,β$ be orientation-preserving homeomorphisms of $[0,\infty]$ onto itself, which have only two fixed points at $0$ and $\infty$, and whose restrictions to $\mathbb{R}_+=(0,\infty)$ are diffeomorphisms, and let $U_α,U_β$ be the corresponding isometric shift operators on the space $L^p(\mathbb{R}_+)$ given by $U_μf=(μ')^{1/p}(f\circμ)$ for $μ\in\{α,β\}$. We prove sufficient conditions for the right and left Fredholmness on $L^p(\mathbb{R}_+)$ of singular integral operators of the form $A_+P_γ^++A_-P_γ^-$, where $P_γ^\pm=(I\pm S_γ)/2$, $S_γ$ is a weighted Cauchy singular integral operator, $…

2017-05-29math.FA

Radial Toeplitz operators on the Fock space and square-root-slowly oscillating sequences

In this paper we show that the C*-algebra generated by radial Toeplitz operators with $L_{\infty}$-symbols acting on the Fock space is isometrically isomorphic to the C*-algebra of bounded sequences uniformly continuous with respect to the square-root-metric $ρ(j,k)=|\sqrt{\vphantom{jk}j}-\sqrt{\vphantom{jk}k}\,|$. More precisely, we prove that the sequences of eigenvalues of radial Toeplitz operators form a dense subset of the latter C*-algebra of sequences.

2015-05-29math.FAmath.OA

更多相关论文收起更多论文

半直线上慢振荡函数格的同态

Homomorphisms of the lattice of slowly oscillating functions on the half-line

研究半直线上慢振荡函数向量格同态空间的结构，证明零同态的特殊性，并给出该空间与半直线乘积空间加一点同胚的刻画。

2024-04-18math.FAmath.GN

Fredholmness and Index of Simplest Weighted Singular Integral Operators with Two Slowly Oscillating Shifts

Let $α$ and $β$ be orientation-preserving diffeomorphisms (shifts) of $\mathbb{R}_+=(0,\infty)$ onto itself with the only fixed points $0$ and $\infty$, where the derivatives $α'$ and $β'$ may have discontinuities of slowly oscillating type at $0$ and $\infty$. For $p\in(1,\infty)$, we consider the weighted shift operators $U_α$ and $U_β$ given on the Lebesgue space $L^p(\mathbb{R}_+)$ by $U_αf=(α')^{1/p}(f\circα)$ and $U_βf= (β')^{1/p}(f\circβ)$. For $i,j\in\mathbb{Z}$ we study the simplest weighted singular integral operators with two shifts $A_{ij}=U_α^i P_γ^++U_β^j P_γ^-$ on $L^p(\mathbb{R…

2014-10-26math.FA

On regularization of Mellin PDO's with slowly oscillating symbols of limited smoothness

We study Mellin pseudodifferential operators (shortly, Mellin PDO's) with symbols in the algebra $\widetilde{\mathcal{E}}(\mathbb{R}_+,V(\mathbb{R}))$ of slowly oscillating functions of limited smoothness introduced in \cite{K09}. We show that if $\mathfrak{a}\in\widetilde{\mathcal{E}}(\mathbb{R}_+,V(\mathbb{R}))$ does not degenerate on the "boundary" of $\mathbb{R}_+\times\mathbb{R}$ in a certain sense, then the Mellin PDO ${\rm Op}(\mathfrak{a})$ is Fredholm on the space $L^p$ for $p\in(1,\infty)$ and each its regularizer is of the form ${\rm Op}(\mathfrak{b})+K$ where $K$ is a compact opera…

2014-07-12math.APmath.FA