学术报告：Fuglede's conjecture in Qp

中科院数学与系统科学研究院

数学研究所

动力系统研究中心

学术报告会

报告人：凡石磊 副教授（华中师大）

题  目：Fuglede's conjecture in Q_p

时  间：02.19（星期五）, 16:00-17:00

地  点：数学院南楼N913室

Abstract:

    I will report on our recent progress in studying Fuglede's conjecture in the filed Q_p of p-adic numbers. We proved that Fuglede's conjecture concerning spectral sets and tilings holds in the field of p-adic numbers, i.e. a Borel set of positive and finite Haar measure is a spectral set if and only if it tiles the space by translation, although the conjecture remains open in the field of real numbers. Our study is based on the investigation of a convolution equation of the form f * \mu =1, where \mu is a measure supported by a discrete set and f is a non-negative integrable function. I. J. Schoenberg's result concerning the p^n-th roots of unity plays a crucial role.