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The measure of the orthogonal polynomials related to Fibonacci chains: the periodic case

Wolfdieter Lang

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The spectral measure for the two families of orthogonal polynomial systems related to periodic chains with N-particle elementary unit and nearest-neighbour harmonic interaction is computed using two different methods. The interest is in the orthogonal polynomials related to Fibonacci chains in the periodic approximation. The relation of the measure to appropriately defined Green's functions is established.


PACS

02.10.De Algebraic structures and number theory

02.30.Gp Special functions

MSC

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (See also 42C05 for general orthogonal polynomials and functions)

11B39 Fibonacci and Lucas numbers and polynomials and generalizations

34B27 Green functions

Subjects

Mathematical physics

Dates

Issue 14 (21 July 1996)

Received 6 June 1995, in final form 30 January 1996


A Corrigendum for this article has been published in 1997 J. Phys. A: Math. Gen. 30 765


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