Multi-tiling and Riesz bases

Seminar
Analysis
Speaker
Dr. Sigrid Grepstad, Norwegian University of Science and Technology
Date
11/03/2013 - 14:00Add to Calendar 2013-03-11 14:00:00 2013-03-11 14:00:00 Multi-tiling and Riesz bases Let S be a bounded, Riemann measurable set in R^d, and L  be a lattice. By a theorem of Fuglede, if S tiles R^d with          translation set L, then S has an orthogonal basis of exponentials.  We show that, under the more general condition that S multi-tiles   R^d with translation set L, S has a Riesz basis of exponentials. The proof is based on Meyer's quasicrystals. This is a joint work with  Nir Lev.                                                            אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Abstract

Let S be a bounded, Riemann measurable set in R^d, and L 
be a lattice. By a theorem of Fuglede, if S tiles R^d with         
translation set L, then S has an orthogonal basis of exponentials. 
We show that, under the more general condition that S multi-tiles  
R^d with translation set L, S has a Riesz basis of exponentials. The
proof is based on Meyer's quasicrystals. This is a joint work with 
Nir Lev.                                                           

Last Updated Date : 04/03/2013