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SUMMARY:Marcin Bownik (University of Oregon)
DTSTART:20211122T190000Z
DTEND:20211122T200000Z
DTSTAMP:20260513T204517Z
UID:paw/40
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/paw/40/">Sim
 ultaneous dilation and translation tilings of $\\R^n$</a>\nby Marcin Bowni
 k (University of Oregon) as part of Probability and Analysis Webinar\n\n\n
 Abstract\nIn this talk we present a solution of the wavelet set problem. T
 hat is\, we characterize full-rank lattices $\\Gamma\\subset \\R^n$ and in
 vertible $n \\times n$ matrices $A$ for which there exists a measurable se
 t $W$ such that $\\{W + \\gamma: \\gamma \\in \\Gamma\\}$ and $\\{A^j(W): 
 j\\in \\Z\\}$ are tilings of $\\R^n$.  The characterization is a non-obvio
 us generalization of the one found by Ionascu and Wang\, which solved the 
 problem in the case  $n = 2$.  As an application of our condition and a th
 eorem of Margulis\, we also strengthen a result of Dai\, Larson\, and the 
 second author on the existence of wavelet sets by showing that wavelet set
 s exist for matrix dilations\, all of whose eigenvalues $\\lambda$ satisfy
  $|\\lambda| \\ge 1$. As another application\, we show that the Ionascu-Wa
 ng characterization characterizes those dilations whose product of two sma
 llest eigenvalues in absolute value is $\\ge 1$.\n> Based on a joint work 
 with Darrin Speegle.\n
LOCATION:https://researchseminars.org/talk/paw/40/
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