# Seminar at SMU Delhi

September 12, 2012 (Wednesday) , 3:30 PM at Webinar
Speaker: Debashish Bose, Institute of Mathematical Sciences, Chennai
Title: Structure of Spectral Pairs in 1-dimension
Abstract of Talk
A bounded measurable set $\Omega \subseteq \mathbb{R}$, is called spectral if there is a set $\Lambda \subseteq \mathbb{R}$ such that the exponential functions $e_\lambda(x) = \exp(2\pi i \lambda x)$, $\lambda\in\Lambda$, form a complete orthonormal system on $L^2(\Omega)$. Such a set $\Lambda$ is called a spectrum of $\Omega$, and the pair $(\Omega,\Lambda)$ is called a spectral pair. Spectral sets have deep relation with Tiling problems. I will talk about structure of spectral pairs in dimension-$1$.