紧群上左不变拉普拉斯算子关于高斯估计和亚椭圆性的扰动结果

IF 0.4 4区数学 Q4 MATHEMATICS

Colloquium Mathematicum Pub Date : 2021-10-14 DOI:10.4064/cm8696-8-2022

Qi Hou, L. Saloff‐Coste

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引用次数: 0

摘要

在本文中，我们研究了紧连通群上的左不变拉普拉斯算子，这些紧连通群是双不变拉普拉斯算子的可比扰动。我们的结果表明，某些双不变拉普拉斯算子所享受的热核导数的高斯界对于其形式可比的扰动是成立的。我们进一步证明了与这种左不变拉普拉斯算子，特别是与双不变拉普拉斯算子相关的抛物算子在各种意义上都是次椭圆的。

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Perturbation results concerning Gaussian estimates and hypoellipticity for left-invariant Laplacians on compact groups

In this paper we study left-invariant Laplacians on compact connected groups that are form-comparable perturbations of bi-invariant Laplacians. Our results show that Gaussian bounds for derivatives of heat kernels enjoyed by certain bi-invariant Laplacians hold for their form-comparable perturbations. We further show that the parabolic operators associated with such left-invariant Laplacians, in particular, with the bi-invariant Laplacians, are hypoelliptic in various senses.

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来源期刊

Colloquium Mathematicum MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Colloquium Mathematicum is a journal devoted to the publication of original papers of moderate length addressed to a broad mathematical audience. It publishes results of original research, interesting new proofs of important theorems and research-expository papers in all fields of pure mathematics. Two issues constitute a volume, and at least four volumes are published each year.