TITLE Approximation by translates of powers of a continuous periodic
function

SPEAKER: Yitzhak Weit, University of Haifa

ABSTRCT: We characterize the set of real-valued, 2pi-periodic, continuous functions f for which the translation invariant subspace V(f) generated by f^n, n geq 0, is dense in C(T) where T denotes the unit circle. In particular, it follows that if f takes a given value at only one point ( which is necessarily its maximum or minimum) then V(f) is
dense in C(T). One observes that V(cos(t)) contains the orthogonal trigonometric
system {cos(kt) ,sin(kt)} hence it is dense in C(T). Our purpose is to characterize the
set of functions which share with cos(t) this propert.