Abstract
A pair (U,V) of Hermitian regular linear functionals on the unit circle is said to be a (1,1)-coherent pair if their corresponding sequences of monic orthogonal polynomials {φn(x)}n≥0 and {ψn(x)}n≥0 satisfy φn[1](z)+anφn-1[1](z)=ψn(z)+bnψn-1(z), an≠0, n≥1, where φn[1](z)=φn+1′(z)/(n+1). In this contribution, we consider the cases when U is the linear functional associated with the Lebesgue and Bernstein-Szegod measures, respectively, and we obtain a classification of the situations where V is associated with either a positive nontrivial measure or its rational spectral transformation.
Original language | English |
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Article number | 307974 |
Journal | Abstract and Applied Analysis |
Volume | 2013 |
DOIs | |
Publication status | Published - 2013 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics