Functional Analysis and Applications Seminar 

17/05/2011, 15:00 — 16:00 — Room P3.10, Mathematics Building
Nikolai Nikolski, University Bordeaux I, France and Steklov Institute of Mathematics, Russia

Approximation problems on the Hilbert Multidisc arising from the Riemann Hypothesis

Completeness of dilation systems $(f(n x))$ with $n \gt 0$ on the standard Lebesgue space $L_2(0,1)$ 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 $H_2(D_2^\infty)$ on the Hilbert multidisc $D_2^\infty$. 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).