- May 17, 2011, Tuesday - 15h00 (Room P
3.10):
Nikolai Nikolski
(University Bordeaux I, France and Steklov Institute of Mathematics,
Russia)
" Approximation
problems on the Hilbert Multidisc arising from the Riemann Hypothesis "
Abstract. Completeness
of dilation systems (f(nx)) with n greater than zero on the standard
Lebesgue space L2(0,1) is considered for 2-periodic functions f. We
show that the problem is equivalent to an open question on cyclic
vectors of the Hardy space H2(D2^∞) on the Hilbert multidisc D2^∞.
Several simple sufficient conditions are exhibited, which contain
however practically all previously known results (Wintner; Kozlov;
Neuwirth, Ginsberg, and Newman; Hedenmalm, Lindquist, and Seip). The
Riemann Hypothesis on zeros of the Euler zeta-function is known to be
equivalent to a completeness of a similar but non-periodic dilation
system (due to Nyman).
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