34 research outputs found
Bernstein's problem on weighted polynomial approximation
We formulate and discuss a necessary and sufficient condition for polynomials
to be dense in a space of continuous functions on the real line, with respect
to Bernstein's weighted uniform norm. Equivalently, for a positive finite
measure on the real line we give a criterion for density of polynomials
in
Pseudocontinuation and cyclicity for random power series
We prove that a random function in the Hardy space is a non-cyclic
vector for the backward shift operator almost surely. The question of existence
of a local pseudocontinuation for a random analytic function is also studied