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

We will discuss a joint result with Nir Lev, which states that for any convex and centrally symmetric polytope $\mathrm{\Omega }\subset {\mathbb{R}}^d$, whose faces of all dimensions are also centrally symmetric, there exists a Riesz basis of exponential functions for $L^2(\mathrm{\Omega })$.
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 $\mathrm{\Omega }$ lie in the lattice ${\mathbb{Z}}^d$.