Technion Analysis seminar Speaker: Adrian Ubis (Hebrew University) Title: Smoothness of Fourier series with polynomial frequencies Date: Thursday, April 19 at 2:30 p.m. Place: Amado 919. Cookies: 10 minutes before the talk Abstract: Let F be the 1-periodic function defined as F(x)=x for |x|<1/2.Let P(t) be any non-linear polynomial with integer coefficients. Consider the 1-periodic function F_P defined by keeping just the Fourier coefficients of F whose frequencies are of the shape P(n) with n an integer. We will show that the smoothness properties of this function are quite complex in the sense that for each s in some interval, the points with Holder exponent s form a set of positive Hausdorff dimension. This was previously known for P a quadratic polynomial, namely for Riemann's example of a continuous but almost nowhere differentiable function. Seminar webpage: <http://www.technion.ac.il/~tamarzr/analysis.html> --------------------------------------------------------- Technion Math. Net (TECHMATH) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Tamar Ziegler <tamarzr@tx.technion.ac.il>