In this paper,we establish a new multivariate Hermite sampling series involving samples from the function itself and its mixed and non-mixed partial derivatives of arbitrary order.This multivariate form of Hermite sam...In this paper,we establish a new multivariate Hermite sampling series involving samples from the function itself and its mixed and non-mixed partial derivatives of arbitrary order.This multivariate form of Hermite sampling will be valid for some classes of multivariate entire functions,satisfying certain growth conditions.We will show that many known results included in Commun Korean Math Soc,2002,17:731-740,Turk J Math,2017,41:387-403 and Filomat,2020,34:3339-3347 are special cases of our results.Moreover,we estimate the truncation error of this sampling based on localized sampling without decay assumption.Illustrative examples are also presented.展开更多
Fabrication technology of the Yb3+:Er3+ co-doped glass samples is introduced. Photolummescence (PL) characteristics of a single sample were experimentally investigated. The PL peak intensities of two samples in series...Fabrication technology of the Yb3+:Er3+ co-doped glass samples is introduced. Photolummescence (PL) characteristics of a single sample were experimentally investigated. The PL peak intensities of two samples in series were measured and discussed. The results show that the PL peak intensities of two samples in series depend on pump manners and arrangement of the samples. The better amplification ability can be obtained by two samples in series doped with low-concentration ytterbium instead of a single sample doped with high-concentration ytterbium.展开更多
This paper investigates double sampling series derivatives for bivariate functions defined on R2 that are in the Bernstein space. For this sampling series, we estimate some of the pointwise and uniform bounds when the...This paper investigates double sampling series derivatives for bivariate functions defined on R2 that are in the Bernstein space. For this sampling series, we estimate some of the pointwise and uniform bounds when the function satisfies some decay conditions. The truncated series of this formula allow us to approximate any order of partial derivatives for function from Bernstein space using only a finite number of samples from the function itself. This sampling formula will be useful in the approximation theory and its applications, especially after having the truncation error well-established. Examples with tables and figures are given at the end of the paper to illustrate the advantages of this formula.展开更多
In this paper an asymptotic formula of Voronovskaja type for a multivariate extension of the Kantorovich generalized sampling series is given. Moreover a quantitative version in terms of some moduli of smoothness is e...In this paper an asymptotic formula of Voronovskaja type for a multivariate extension of the Kantorovich generalized sampling series is given. Moreover a quantitative version in terms of some moduli of smoothness is established. Finally some particular examples of kernels are discussed, as the Bochner-Riesz kernel and the multivariate splines.展开更多
文摘In this paper,we establish a new multivariate Hermite sampling series involving samples from the function itself and its mixed and non-mixed partial derivatives of arbitrary order.This multivariate form of Hermite sampling will be valid for some classes of multivariate entire functions,satisfying certain growth conditions.We will show that many known results included in Commun Korean Math Soc,2002,17:731-740,Turk J Math,2017,41:387-403 and Filomat,2020,34:3339-3347 are special cases of our results.Moreover,we estimate the truncation error of this sampling based on localized sampling without decay assumption.Illustrative examples are also presented.
基金This work was supported by the National Natural Science Foundation of China(No.6988701),Science and Technology Commission of Liaoning Province (No.20022110) Educational Commission of Liaoning Province(No.202123198)
文摘Fabrication technology of the Yb3+:Er3+ co-doped glass samples is introduced. Photolummescence (PL) characteristics of a single sample were experimentally investigated. The PL peak intensities of two samples in series were measured and discussed. The results show that the PL peak intensities of two samples in series depend on pump manners and arrangement of the samples. The better amplification ability can be obtained by two samples in series doped with low-concentration ytterbium instead of a single sample doped with high-concentration ytterbium.
文摘This paper investigates double sampling series derivatives for bivariate functions defined on R2 that are in the Bernstein space. For this sampling series, we estimate some of the pointwise and uniform bounds when the function satisfies some decay conditions. The truncated series of this formula allow us to approximate any order of partial derivatives for function from Bernstein space using only a finite number of samples from the function itself. This sampling formula will be useful in the approximation theory and its applications, especially after having the truncation error well-established. Examples with tables and figures are given at the end of the paper to illustrate the advantages of this formula.
文摘In this paper an asymptotic formula of Voronovskaja type for a multivariate extension of the Kantorovich generalized sampling series is given. Moreover a quantitative version in terms of some moduli of smoothness is established. Finally some particular examples of kernels are discussed, as the Bochner-Riesz kernel and the multivariate splines.
