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Analysis Seminar

Thursday, March 1, 2018 - 3:00pm

Azita Mayeli

CUNY Graduate Center


University of Pennsylvania


Abstract: In 1974, Fuglede conjectured that any bounded set $\Omega$ in $\Bbb R^d$,  with positive measure, tiles $\Bbb R^d$ by countable many translations if and only if $L^2(\Omega)$ has an orthogonal exponential basis. The conjecture was disproved by T. Tao in 2003 in dimensions $d=5$ and higher, followed by results of other people, where the conjecture was disproved in dimension 3 and 4.   In this talk we shall look at the finite version of this conjecture and show that the conjecture holds in $\Bbb Z_p^2$, $p$ prime