The Euler--Lagrange theory for Schur's algorithm: algebraic exposed points (Q2369542)

The author employs algebraic number theory tools to demonstrate that any set of closed arcs on the circle supports a quadratic measure and that any algebraic measure is either a Szegö measure or a measure supported by a proper subset of the unit circle consisting of a finite number of closed arcs. The author exploits the correspondence between number-theoretic problems and orthogonal polynomials, a correspondence already realized by continued fractions.