Speaker: Alon Agin (Tel Aviv University)
Abstract: Akhunzhanov and Shatskov defined the Dirichlet spectrum, corresponding to mxn matrices and to norms on R^m and R^n. In case (m,n) = (2,1) and using the Euclidean norm on R^2, they showed that the spectrum is an interval. We generalize this result to arbitrary (m,n) with max(m,n)>1 and arbitrary norms, improving previous works from recent years. We also define some related spectra and show that they too are intervals. We also prove the existence of matrices exhibiting special properties with respect to their uniform exponent. Our argument is a modification of an argument of Khintchine from 1926.
Time: Mar 4, 14:00
Room: 1710
Zoom link: https://us06web.zoom.us/j/4233178953?pwd=hafcWWABKH14FtvpFiIcFecKDX9vLr.1&omn=85137639703
Meeting ID: 423 317 8953
Passcode: SIMIS
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