圖上的熱核估計

Abstract

本文討論了歐氏空間與流形上之熱核估計，研究圖上相應條件下之離散熱核估計，並引進連續時間之熱核，藉此引導出離散熱核估計。方便起見，第二章收錄了常用的術語、符號、估計及重要的不等式與條件。文章最後介紹了一些高斯估計的成立條件與推導過程。

The presenting work investigates into the heat kernel bounds in Euclidean spaces and on manifolds, and studies discrete heat kernel bounds on graphs under corresponding conditions. We introduce continuous time heat kernels and derive discrete heat kernel bounds from the its result. For convenience, we collect some common terminology and symbols in this topic in chapter two, and introduce some type of heat kernel bounds and some conditions and inequalities. Finally, we introduce some conditions for the Gaussian bounds and how they can be proved.