一、报告题目：HIGHER DIMENSIONAL VERSIONS OF THE DOUGLAS-AHLFORS
IDENTITIES and DIRICHLET SPACES IN BALLS AND HALF-SPACES OF Rn
二、报告人：钱涛 教授
三、时 间：2025年4月23日（周三）15:00—16:00
四、地 点：A4-309
报告摘要：In 1930’s Douglas established identical relations between a group of quantities in the unit disc, by which he solved Plateau’s minimum surface problem. Later Ahlfors joined the study and provided some identical relations in terms of complex holomorphic functions. Based on a quantity he introduced he reproved the hard part of the Douglas identities. Nowadays it is realised that those identical quantities are different expressions of the semi-norm of the Dirichlet space for the unit disc. Our talk generalises the quantities and the identical relations, as well as the Dirichlet space theme to all types of balls and upper-half Euclidean spaces.
报告人简介：钱涛，澳门科技大学教授，博士生导师。澳门数学研究中心主任，澳门科技大学数学系主任。1984年博士毕业于北京大学。1984-2019年先后工作于中科院数学所、Macquarie 大学 、Flinders大学、New England 大学、澳门大学。研究兴趣包括调和分析、(随机)信号分析、(超)复分析等。迄今为止在Automatica、Math. Ann.、J. Funct. Anal.、Tran. Amer. Math, Soc.、IEEE Transactions on Automatic Control、IEEE Transactions on Image Processing国际知名期刊上发表论文200多篇，出版专著2部，主持科研项目30余项， 2012年获澳门科学技术奖自然科学一等奖，担任Math. Meth. Appli. Sci.、Complex Anal. Oper. Theory、Complex Varia. Ellip. Equations等SCI杂志主编。多次组织举办具有影响力的国际学术会议，与多国数学家有广泛合作与交流。
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