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

Speaker：Fan Shilei Associate professor（Central China Normal University ）

Title：Fuglede's conjecture in Q_p

Time：02.19, 16:00-17:00

Venue：N913

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.