Mate-Nevai-Totik theorem for Krein systems

Abstract

We prove the Cesàro boundedness of eigenfunctions of the Dirac operator on the half-line with a square-summable potential. The proof is based on the theory of Krein systems and, in particular, on the continuous version of a theorem by A.

Entropy function and orthogonal polynomials

“…This and (Jensen's) inequality e P(log w,zn) P n (ξ 0 ) gives us the upper bound in (13). The lower bound in ( 13) is just a combination of estimates (10), (11).…”

“…Closing this section, let us comment on the continuous version of the problem. Recently P. Gubkin [13] proved a variant of Theorem 1 for Krein's systems. His proof follows the line of A. Máté, P. Nevai and V. Totik [18].…”