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>
 
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Technion Math. Net (TECHMATH)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Tamar Ziegler   <tamarzr@tx.technion.ac.il>