Abstract:
In 1977, F. G. Aroutyunyan proved that every continuous function on the unit
circle, after a change on a set of arbitrarily small measure, acquires a
uniformly convergent Fourier series and large gaps in the spectrum. Later,
this version of the classical Men'shov correction theorem underwent
several generalizations and refinements (partly, this was done by the
author).
In the talk we will review some of these results. The emphasis will be on
the borders for the validity of the uncertainty principle (“a function and
its Fourier transform cannot be too small simultaneously”) and on sharp
estimates in correction theorems similar to those mentioned above.
