A Tauberian approach to an analog of Weyl’s law for the Kohn Laplacian on compact Heisenberg manifolds
A Tauberian approach to an analog of Weyl’s law for the Kohn Laplacian on compact Heisenberg manifolds
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紧海森堡流形上科恩拉普拉斯算子Weyl定律的陶伯法模拟
DOI：
10.1007/s40627-022-00094-3
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Zeytuncu, Yunus E.
中科院分区：
文献类型：
--
作者：
Fan, Colin;Kim, Elena;Zeytuncu, Yunus E.
Letbe a compact quotient of thed-dimensional Heisenberg groupby a lattice subgroup. We show that the eigenvalue counting function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N^\alpha \left( \lambda \right) $$\end{document} for any fixed element of a family of second order differential operators \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\{ \mathcal {L}_\alpha \right\} $$\end{document} onMhas asymptotic behavior \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N^\alpha \left( \lambda \right) \sim C_{d,\alpha } {\text {vol}}\left( M\right) \lambda ^{d + 1}$$\end{document}, whereis a constant that only depends on the dimensiondand the parameter. As a consequence, we obtain an analog of Weyl’s law (both on functions and forms) for the Kohn Laplacian onM. Our main tools are Folland’s description of the spectrum ofand Karamata’s Tauberian theorem.
Letbe a compact quotient of thed-dimensional Heisenberg groupby a lattice subgroup. We show that the eigenvalue counting function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N^\alpha \left( \lambda \right) $$\end{document} for any fixed element of a family of second order differential operators \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\{ \mathcal {L}_\alpha \right\} $$\end{document} onMhas asymptotic behavior \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N^\alpha \left( \lambda \right) \sim C_{d,\alpha } {\text {vol}}\left( M\right) \lambda ^{d + 1}$$\end{document}, whereis a constant that only depends on the dimensiondand the parameter. As a consequence, we obtain an analog of Weyl’s law (both on functions and forms) for the Kohn Laplacian onM. Our main tools are Folland’s description of the spectrum ofand Karamata’s Tauberian theorem.
紧凑型海森堡流形作为 CR 流形
DOI：
10.1007/bf02922102
发表时间：
2004
期刊：
The Journal of Geometric Analysis
影响因子：
--
作者：
G. Folland
通讯作者：
G. Folland
球体上科恩拉普拉斯算子的韦尔定律的陶伯方法
DOI：
10.4153/s0008439521000163
发表时间：
2022
期刊：
Canadian Mathematical Bulletin
影响因子：
--
作者：
Bosch, Henry;Gonzales, Tyler;Spinelli, Kamryn;Udell, Gabe;Zeytuncu, Yunus E.
通讯作者：
Zeytuncu, Yunus E.