报告人：赵健（贵州财经大学）

时间：2024年09月20日 10:00-

地址：数统学院LD402

摘要：In this talk, we mainly introduce the heat transform $H_tf$ of f on the complex plane C. First, we introduce the relevant notations and definitions covered in this talk. Second, we introduce the limit behavior of the heat transform $H_tf$ of f on the complex plane C as t goes to infinity. We show that, under certain conditions on f, $H_tf(z)$ converges pointwise on C if and only if there exists a harmonic function h on C such that $H_tf(z)$ converges to h(z) uniformly on compact subsets of C. For non-negative functions f, we obtain several equivalent conditions on f such that $H_tf$ converges to 0 uniformly on C. In particular, we show that, for non-negative and bounded f on C, $H_tf$ converges to 0 uniformly on C if and only if f is a vanishing probability distribution function. Finally, we introduce the continuous embedding of the heat transform $H_tf$ for f in $L^p(d\mu_{t_0})$ on the complex plane C. We obtain the sufficient and necessary condition of the continuous embedding of the heat transform $H_t$.

简介：赵健，男，汉族，理学博士。主要研究方向为解析函数空间理论与算子理论。

邀请人：秦越石、王奕、王子鹏、晏福刚、赵显锋

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