Functional analysis, orthogonal polynomials and a theorem of Markov (1988)
The connection between functional analysis and the classical theory of orthogonal polynomials is explored in detail, at least in the bounded case. A functional analytic proof of Markov's theorem, the main link between the two subjects, is given. A special case of Darboux's asymptotic method is presented, and an example showing the ~ower of asymptotic methods to determine orthogonality measures of systems defined by three terms recurrence relations is included.