Rocky mountain journal of mathematics vol:21 issue:1 pages:501-527
An elementary approach is given to prove Blumenthal's theorem describing the support of measures associated with orthogonal polynomials on the real line in case the recurrence coefficients associated with these polynomials tend to finite limits. Then the known approach using H. Weyl's theorem on compact perturbations of self-adjoint operators to Blumenthal's theorem is presented. Finally, using Weyl's theorem, Geronimus's result on the support is discussed when the recurrence coefficients with subscripts having the same residue (mod k) have finite limits. Instead of the usual approach of using continued fractions, the Hardy class H-2 is used to determine the spectrum of the self-adjoint operator arising in the study of this support.