Heat Content for Stable Processes in Domains of \(\mathbb {R}^d\)

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• 作者：Luis Acuña Valverde
• 关键词：Stable processes ; Heat kernels ; Heat content ; Heat trace ; Expansions
• 刊名：The Journal of Geometric Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：27
• 期：1
• 页码：492-524
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Differential Geometry; Convex and Discrete Geometry; Fourier Analysis; Abstract Harmonic Analysis; Dynamical Systems and Ergodic Theory; Global Analysis and Analysis on Manifolds;
• 出版者：Springer US
• ISSN：1559-002X
• 卷排序：27

文摘

This paper studies the small time behavior of the heat content for rotationally invariant \(\alpha \)-stable processes, \(0<\alpha \le 2\), in domains of \(\mathbb {R}^d\). Unlike the asymptotics for the heat trace, the behavior of the heat content differs depending on the range of \(\alpha \) according to \(0<\alpha <1\), \(\alpha =1\) and \(1<\alpha \le 2\).