Action of the Infinite Torus
Sunday, March 9, 2014
 
In this exercise we introduce the action of the infinite product of the torus on the Fourier coefficients of a periodic function. We equip this infinite torus T∞ with a diffeology we call “tempered” and show that its action on the space of Fourier coefficients is then smooth. We exhibit then an irrational solenoid in T∞. Ref. http://math.huji.ac.il/~piz/documents/DBlog-Ex-ITAOSPF.pdf