Blumenthal's Theorem for Laurent Orthogonal Polynomials

Monotonicity of Zeros of Orthogonal Laurent Polynomials

Monotonicity of zeros of orthogonal Laurent polynomials associated with a strong distribution with respect to a parameter is discussed. A natural analog of a classical result of A. Markov is proved. Recent results of Ismail and Muldoon based on the Hellman-Feynman theorem are also extended to a monotonicity criterion for zeros of Laurent polynomials. Results concerning the behaviour of extreme ...

Nonsymmetric Askey-Wilson polynomials and Q-polynomial distance-regular graphs

In his famous theorem (1982), Douglas Leonard characterized the q-Racah polynomials and their relatives in the Askey scheme from the duality property of Q-polynomial distance-regular graphs. In this paper we consider a nonsymmetric (or Laurent) version of the q-Racah polynomials in the above situation. Let Γ denote a Q-polynomial distance-regular graph that contains a Delsarte clique C. Assume ...

. C A ] 1 4 Fe b 19 95 ORTHOGONAL POLYNOMIALS AND LAURENT POLYNOMIALS RELATED TO THE HAHN - EXTON q - BESSEL FUNCTION

Laurent polynomials related to the Hahn-Exton q-Bessel function, which are qanalogues of the Lommel polynomials, have been introduced by Koelink and Swarttouw. The explicit strong moment functional with respect to which the Laurent q-Lommel polynomials are orthogonal is given. The strong moment functional gives rise to two positive definite moment functionals. For the corresponding sets of orth...

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Five-diagonal Matrices and Zeros of Orthogonal Polynomials on the Unit Circle

It is shown that monic orthogonal polynomials on the unit circle are the characteristic polynomials of certain five-diagonal matrices depending on the Schur parameters. This result is achieved through the study of orthogonal Laurent polynomials on the unit circle. More precisely, it is a consequence of the five term recurrence relation obtained for these orthogonal Laurent polynomials, and the ...