6 Maggio, 2022 14:00
Sezione di Geometria, Algebra e loro applicazioni
Riesz basis of exponentials for convex polytopes with symmetric faces
Alberto Debernardi Pinos, Università di Aveiro
Aula Seminari del terzo piano
Abstract
We will discuss a joint result with Nir Lev, which states that for any convex and centrally symmetric polytope $\Omega\subset \mathbb{R}^d$, whose faces of all dimensions are also centrally symmetric, there exists a Riesz basis of exponential functions for $L^2(\Omega)$.
This result extends previously known statements in this direction due to Lyubarskii and Rashkovskii, and also due to Walnut ($d=2$), and by Grepstad and Lev (in arbitrary dimensions), where the same conclusion is obtained under the additional assumption that all the vertices of $\Omega$ lie in the lattice $\mathbb{Z}^d$.