Reproducing kernel Hilbert spaces via sampling in discrete spaces

被引:0
|
作者
Mohammadreza Foroutan
Raheleh Asadi
机构
[1] Payame Noor University,Department of Mathematics
[2] University College of Omran-Toseeh,Faculty of Human Sciences
来源
The Journal of Analysis | 2023年 / 31卷
关键词
-valued reproducing kernels; Laplace operator; Multiplication operator; Relative ; -valued reproducing kernels; 46E22; 47B32;
D O I
暂无
中图分类号
学科分类号
摘要
This paper explores the reproducing property of some Hilbert spaces of functions from set X to some linear space E and discusses the essential ideas behind such space along with their applications in sampling theory and machine learning. We extend the idea of E-valued reproducing kernel Hilbert spaces to scalar case as considering X×E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X\times E$$\end{document} instead of the set X, where E is a linear space. Our investigation focuses on vector-valued reproducing kernel function spaces without the condition of Hilbert spaces on E. We concentrate on two concepts: E-valued reproducing kernels and relative E-valued reproducing kernels, and in particular we characterize reproducing kernel Hilbert spaces by multipliers and then focus on finite graphs and find Laplace operator.
引用
收藏
页码:1805 / 1818
页数:13
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