Authors:Jerome GİLLES Abstract: Recently, the construction of 2D empirical wavelets based on partitioning the Fourier domain with the watershed transform has been proposed. If such approach can build partitions of completely arbitrary shapes, for some applications, it is desirable to keep a certain level of regularity in the geometry of the obtained partitions. In this paper, we propose to build such partition using Voronoi diagrams. This solution allows us to keep a high level of adaptability while guaranteeing a minimum level of geometric regularity in the detected partition. PubDate: Thu, 01 Dec 2022 00:00:00 +030
Authors:Borislav DRAGANOV Abstract: We construct a sampling operator with the property that the smoother a function is, the faster its approximation is. We establish a direct estimate and a weak converse estimate of its rate of approximation in the uniform norm by means of a modulus of smoothness and a $K$-functional. The case of weighted approximation is also considered. The weights are positive and power-type with non-positive exponents at infinity. This sampling operator preserves every algebraic polynomial. PubDate: Thu, 01 Dec 2022 00:00:00 +030
Authors:Jorge BUSTAMANTE Abstract: We present an estimate for the rate of convergence of Mihesan operators in polynomial weighted spaces. A Voronovskaja-type theorem is included. PubDate: Thu, 01 Dec 2022 00:00:00 +030
Authors:Ramazan AKGÜN Abstract: Present work contains a method to obtain Jackson and Stechkin type inequalities of approximation by integral functions of finite degree (IFFD) in some variable exponent Lebesgue space of real functions defined on $\boldsymbol{R}:=\left( -\infty ,+\infty \right) $. To do this, we employ a transference theorem which produce norm inequalities starting from norm inequalities in $\mathcal{C}(\boldsymbol{R})$, the class of bounded uniformly continuous functions defined on $\boldsymbol{R}$. Let $B\subseteq \boldsymbol{R}$ be a measurable set, $p\left( x\right) :B\rightarrow \lbrack 1,\infty )$ be a measurable function. For the class of functions $f$ belonging to variable exponent Lebesgue spaces $L_{p\left( x\right) }\left( B\right) $, we consider difference operator $\left( I-T_{\delta }\right)^{r}f\left( \cdot \right) $ under the condition that $p(x)$ satisfies the log-Hölder continuity condition and $1\leq \mathop{\rm ess \; inf} \limits\nolimits_{x\in B}p(x)$, $\mathop{\rm ess \; sup}\limits\nolimits_{x\in B}p(x)<\infty $, where $I$ is the identity operator, $r\in \mathrm{N}:=\left\{ 1,2,3,\cdots \right\} $, $\delta \geq 0$ and $$ T_{\delta }f\left( x\right) =\frac{1}{\delta }\int\nolimits_{0}^{\delta }f\left( x+t\right) dt, x\in \boldsymbol{R}, T_{0}\equiv I, $$ is the forward Steklov operator. It is proved that $$ \left\Vert \left( I-T_{\delta }\right) ^{r}f\right\Vert _{p\left( \cdot \right) } $$ is a suitable measure of smoothness for functions in $L_{p\left( x\right) }\left( B\right) $, where $\left\Vert \cdot \right\Vert _{p\left( \cdot \right) }$ is Luxemburg norm in $L_{p\left( x\right) }\left( B\right) .$ We obtain main properties of difference operator $\left\Vert \left( I-T_{\delta }\right) ^{r}f\right\Vert _{p\left( \cdot \right) }$ in $L_{p\left( x\right) }\left( B\right) .$ We give proof of direct and inverse theorems of approximation by IFFD in $L_{p\left( x\right) }\left( \boldsymbol{R}\right) . $ PubDate: Thu, 01 Dec 2022 00:00:00 +030
Authors:Rosario CORSO Abstract: This paper concerns dual frames multipliers, i.e. operators in Hilbert spaces consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames, respectively. The goal of the paper is to give some results about the localization of the spectra of dual frames multipliers, i.e. to identify regions of the complex plane containing the spectra using some information about the frames and the symbols. PubDate: Thu, 01 Dec 2022 00:00:00 +030
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