Nonnegative linearization for little q-Laguerre polynomials and Faber basis

摘要

The support of the orthogonality measure of so-called little q-Laguerre polynomials {l(n) (.; a vertical bar q)}(n=0)(infinity), 0 < q < 1, 0 < a < q(-1), is given by S-q = {1, q, q(2),...} boolean OR {0}. Based on a method of Mlotkowski and Szwarc we deduce a parameter set which admits nonnegative linearization. Moreover, we use this result to prove that little q-Laguerre polynomials constitute a so-called Faber basis in C(S-q). (c) 2005 Elsevier B.V. All rights reserved.