报告题目1：NON-STANDARD SINGULAR INTEGRALS ASSOCIATED WITH MIXED HOMOGENEITIES

报告人：韩永生教授，美国Auburn大学

报告时间：2023年12月26日（周二）8:30

报告地点：20-306

报告摘要：Phong and Stein introduced non-standard convolution singular integrals with mixed ho-mogeneities. Let R^{n} = R^{n−1} × R with x = (x’, xn) ∈ R^{n−1} × R. Set |x|_{e} = (|x’|2 + |x_{n}|2)^{1/2} and |x|_{h} = (|x’|2 + |x_{n}|)^{1/2}. These two metrics correspond to the following two types of dilations:

(1) the classical isotropic dilations:δe : (x’, x_{n}) → (δx’, δx_{n}), δ> 0.

(2) the non-isotropic dilations:δh : (x’, x_{n}) → (δx’,δ^{2}x_{n}), δ> 0.

Suppose that E_{k}(x) is homogeneous of degree −k in the isotropic sense near the orgin, that is, δ^{k}E_{k}(δ_{e}x) = E_{k}(x) and similarly, Hℓ(x) is homogeneous of degree −ℓ in the non-isotropic sense near the orgin, that is, δℓHℓ(δhx) = Hℓ(x).

We consider the boundedness for Phong and Stein’s non-standard convolution singular integrals with the kernel K(x) = E_{k}(x)Hℓ(x) for small x and otherwise K is smooth and has compact support, and non-convolution singular integrals with the kernel K(x, y) =E_{k}(x, y)Hℓ(x, y) for small x and otherwise K is smooth and has compact support.

报告人简介：韩永生教授1981年于北京大学获得硕士学位，1984年在美国Washington University大学师从鼎鼎大名的调和分析大师G. Weiss 教授，获得博士学位。目前，他是美国Auburn大学数学系终身教授。韩永生教授长期从事调和分析的教学与研究，尤其是函数空间理论，已在国内外期刊 Trans. Amer. Math. Soc., Forum Math., Ann. Scuola Norm. Sup. Pisa Cl. Sci., J. Geometric Analysis, Journal of Functional Analysis,  Revista Mathematica Iberoamericana, Analysis and PDE, Mem. Amer. Math. Soc., Math. Z.等杂志发表学术论文。撰写出版专著《Harmonic Analysis on Spaces of Homogeneous Type》，《Hp空间》，《近代调和分析方法及其应用》。

报告题目2：Barron Space for Graph Convolution Neural Networks

报告人：孙颀彧教授，University of Central Florida

报告时间：2023年12月26日（周二）9:40

报告地点：20-306

报告摘要：Graph convolutional neural network  (GCNN) operates on graph domain and it has  achieved a superior performance to accomplish a wide range of tasks. In this talk, we introduce a Barron space of functions on a compact domain of graph signals, discuss its various properties, such as reproducing kernel Banach space property and universal approximation property. We will also discuss well approximation property of functions in the Barron space by outputs of some GCNNs, and learnability of functions in the Barron space from their random samples.

报告人简介：孙颀彧教授主要从事傅里叶分析、小波分析、框架理论、信号采样和处理等方面的研究工作。在国际顶尖权威杂志 Memoirs of American Mathematical Society, Transaction of American Mathematical Society, Applied and Computational Harmonic Analysis, Advances in Computational Mathematic, IEEE Transaction on Information Theory, IEEETransaction on Signal Processing, Journal of Fourier Analysis and Applications等发表论文100多篇。担任Journal of Fourier Analysis and Applications, Sampling Theory in Signal and Imaging Processing, Numerical Functional Analysisand Optimization等期刊的编委。

报告题目3：Lp boundedness for the Calderon commutator with rough kernels of GS type

报告人：陶祥兴教授，浙江科技大学

报告时间：2023年12月26日（周二）10:50

报告地点：20-306

报告摘要：Let \Omega be homogeneous of degree zero, integrable on the unit sphere, and have vanishing moment of order k, and T_{\Omega, a, k} be the d-dimensional Calderon commutator with Lipschitz function a. In this talk, we will show the lines of the proof of the Lp boundedness for the above Calderon commutators with rough kernel of the GS_\beta type. This is joint work with J. Chen and G. Hu.

报告人简介：陶祥兴，浙江科技大学教授，博士生导师，二级教授，主持完成国家自然科学基金多项，目前主持国家自然科学基金项目1项。现任浙江科技大学理学院院长，应用数学研究所所长，浙江省高校数学教学指导委员会副主任，浙江省数理医学研究会常务理事等。