Local Bernstein theory, and lower bounds for Lebesgue constants

I’ve just uploaded to the arXiv my paper “Local Bernstein theory, and lower bounds for Lebesgue constants“. This paper was initially motivated by a problem of Erdős} on Lagrange interpolation, but in the course of solving that problem, I ended up modifying some very classical arguments of Bernstein and his contemporaries (Boas, Duffin, Schaeffer, Riesz, etc.) to obtain “local” versions of these classical “Bernstein-type inequalities” that may be of independent interest. Bernstein proved many est...