Norms of certain functions of a distinguished Laplacian on the $$ax+b$$ groups
Norms of certain functions of a distinguished Laplacian on the $$ax+b$$ groups
复制标题
$$ax b$$ 群上杰出拉普拉斯算子的某些函数的范数
DOI：
10.1007/s00209-022-03143-z
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发表时间：
2022
影响因子：
0.8
通讯作者：
Akylzhanov R
中科院分区：
文献类型：
--
作者：
Akylzhanov R
The aim of this paper is to find new estimates for the norms of functions of a (minus) distinguished Laplace operatoron the ‘’ groups. The central part is devoted to spectrally localized wave propagators, that is, functions of the type, with. We show that for, the convolution kernelof this operator satisfies \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \Vert k_t\Vert _1\asymp t, \qquad \Vert k_t\Vert _\infty \asymp 1, \end{aligned}$$\end{document}so that the upper estimates of D. Müller and C. Thiele (Studia Math., 2007) are sharp. As a necessary component, we recall the Plancherel density ofand spend certain time presenting and comparing different approaches to its calculation. Using its explicit form, we estimate uniform norms of several functions of the shifted Laplace-Beltrami operator, closely related to. The functions include in particular,, and, with complexz,s.
The aim of this paper is to find new estimates for the norms of functions of a (minus) distinguished Laplace operatoron the ‘’ groups. The central part is devoted to spectrally localized wave propagators, that is, functions of the type, with. We show that for, the convolution kernelof this operator satisfies \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \Vert k_t\Vert _1\asymp t, \qquad \Vert k_t\Vert _\infty \asymp 1, \end{aligned}$$\end{document}so that the upper estimates of D. Müller and C. Thiele (Studia Math., 2007) are sharp. As a necessary component, we recall the Plancherel density ofand spend certain time presenting and comparing different approaches to its calculation. Using its explicit form, we estimate uniform norms of several functions of the shifted Laplace-Beltrami operator, closely related to. The functions include in particular,, and, with complexz,s.