Complexity of Monte Carlo integration for Besov classes on the unit sphereSpringer Science and Business Media LLC - Tập 14 - Trang 1-18 - 2022
Liqin Duan, Peixin Ye, Wan Li
We obtain the exact orders of the complexity of the integration of functions from Besov classes
$$BB_{p,\theta }^\Omega$$
on the unit sphere of d-dimensional Euclidean space in the deterministic and randomized settings. The corresponding optimal quadrature rules have been constructed in both setti...... hiện toàn bộ
The extension problem in free harmonic analysisSpringer Science and Business Media LLC - Tập 13 - Trang 1-27 - 2022
Peter Burton, Kate Juschenko
This paper studies certain aspects of harmonic analysis on nonabelian free groups. We focus on the concept of a positive definite function on the free group and our primary goal is to understand how such functions can be extended from balls of finite radius to the entire group. Previous work showed that such extensions always exist and we study the problem of simultaneous extension of multiple pos...... hiện toàn bộ
Properties of two unitary operator functions involving idempotentsSpringer Science and Business Media LLC - Tập 11 - Trang 540-554 - 2019
Jiaxin Zhang, Jiajia Niu, Yuan Li
Let P be an idempotent operator on a Hilbert space
$$\mathcal {H}.$$
We denote two unitary operator functions
$$U_{\lambda }$$
and
$$V_{\lambda }$$
by
$$\begin{aligned} U_{\lambda }:=(\lambda P+I)|\lambda P+I|^{-1} \hbox { } \hbox { and }\hbox { } V_{\lambda }:=(\lambda P^{*}+I)|\lambda P^{*}+I|^{-1}, \ \ \hbox { for }\lambda \in \mathbb {C}\backslash \{-1\}. \end{aligned}$$
In this pap...... hiện toàn bộ
2-Local uniform isometries between complex Lipschitz algebrasSpringer Science and Business Media LLC - Tập 11 Số 2 - Trang 406-422 - 2020
Alimohammadi, Davood, Bagheri, Reyhaneh
Let (X, d) be a metric space and let $$\mathrm{Lip}(X,d) $$ denote the complex algebra of all complex-valued bounded functions f on X for which f is a Lipschitz function on $$\mathrm{(X,d)}$$. In this paper we give a complete description of all 2-local real and complex uniform isometries between $$\mathrm{Lip}(X,d) $$ and $$\mathrm{Lip(Y},\rho \mathrm{)}$$, where (X, d) and $$(Y,\rho )$$...... hiện toàn bộ
Rough Hausdorff operators on Lebesgue spaces with variable exponentSpringer Science and Business Media LLC - Tập 14 - Trang 1-17 - 2023
Ziwei Li, Jiman Zhao
In this paper, we study rough Hausdorff operators on variable exponent Lebesgue spaces in the setting of the Heisenberg group. We prove the boundedness of rough Hausdorff operators by giving some sufficient conditions.
The consistency and the general common solution to some quaternion matrix equationsSpringer Science and Business Media LLC - Tập 14 - Trang 1-22 - 2023
Xi-Le Xu, Qing-Wen Wang
In this paper, we establish some necessary and sufficient conditions for the solvability to a system of five quaternion matrix equations in terms of the Moore–Penrose inverse and the rank of a matrix, and give an expression of the general solution to the system when it is consistent. As an application, we investigate an
$$\eta $...... hiện toàn bộ