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Discrete inequalities, orthogonal polynomials and the spectral theory of difference operators. (English) Zbl 0761.39007

It was shown in a recent paper of the first two authors that the validity of Copson’s inequality and the value of the best constant are determined in terms of the so-called Hellinger-Nevanlinna \(m\)-function. The theory is the discrete analogue of that established by the second author and W. N. Everitt for a class of integro-differential inequalities [ibid. 380, 447-486 (1982; Zbl 0487.26005)].
In this paper the properties of the \(m\)-function are investigated and connections with the theory of orthogonal polynomials and the Hamburger moment problem are explored. The results are applied to give examples of the series inequalities associated with the classical orthogonal polynomials.

MSC:

39A70 Difference operators
26D10 Inequalities involving derivatives and differential and integral operators
44A60 Moment problems

Citations:

Zbl 0487.26005
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