Aymptotic expansions of fundamental solutions to heat equations and their apllications

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540189
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: University of Hyogo
• Principal Investigator: IWASAKI Chisato 兵庫県立大学, 物質理学研究科, 特命教授 (30028261)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 熱方程式 / 基本解 / 冪零リー群 / スペクトルゼータ函数 / subelliptic作用素 / 擬微分作用素 / Fokker-Planck作用素 / 国際研究者交流、ドイツ、USA

Outline of Final Research Achievements

I have researched methods of construction of the fundamental solution for heat equations corresponding to various kinds of subelliptic operators. This research is applicable to analyze both eigenvalues of operators and singularity of spectral zeta functions of subelliptic operators. Objects subelliptic operators of my research are the Fokker-Planck operator, subelliptic operators on spheres, operators on Nilpotent Lie groups.
In addition to this kind research I succeded to get the precise expression of the fundamental solution to degenerate elliptic operators, which are called operators of Grushin type. This study depends on theories of the modified Bessel functions. I show this method is also useful to study of Kohn-Laplacian which is deeply interested in complex analysis.
These results are published in six papers during the term of this aid.

Free Research Field

偏微分方程式