Vol. 22, No. 3, 1967

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On constructing distribution functions: A bounded denumerable spectrum with n limit points

Daniel Paul Maki

Vol. 22 (1967), No. 3, 431–452
Abstract

If {an}0 and {bn}1 are real sequences with the bn’s all positive, then a theorem of Favard states that there exists a bounded increasing function ψ(x) which is a distribution function for the polynomial set {ϕn}1 which is recursively defined as follows: ϕ1(x) 00(x) 1,

ϕn+1 (x) = (x − an)ϕn(x)− bnϕn−1(x ) (n ≧ 0).

This study considers the problem of constructing ψ(x) for certain classes of sequences {an}0 and {bn}1. The sequences considered all lead to functions ψ(x) which have a bounded denumerable spectrum with n limit points (1 n < ).

Mathematical Subject Classification
Primary: 42.15
Milestones
Received: 14 July 1966
Published: 1 September 1967
Authors
Daniel Paul Maki