Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Ratio and relative asymptotics of polynomials orthogonal on an arc of the unit circle
Journal of Approximation Theory
The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients
Journal of Approximation Theory
Denisov's theorem on recurrence coefficients
Journal of Approximation Theory
Error bounds for rational quadrature formulae of analytic functions
Numerische Mathematik
Relative asymptotic of multiple orthogonal polynomials for Nikishin systems
Journal of Approximation Theory
| Hi-index | 0.00 |
Let µ be a finite positive Borel measure with compact support consisting of an interval [c, d] ⊂ R plus a set of isolated points in R[c, d], such that µ' 0 almost everywhere on [c, d]. Let {w2n}, n ∈ Z+, be a sequence of polynomials, deg w2n ≤ 2n, with real coefficients whose zeros lie outside the smallest interval containing the support of µ. We prove ratio and relative asymptotics of sequences of orthogonal polynomials with respect to varying measures of the form dµ/w2n. In particular, we obtain an analogue for varying measures of Denisov's extension of Rakhmanov's theorem on ratio asymptotics. These results on varying measures are applied to obtain ratio asymptotics for orthogonal polynomials with respect to fixed measures on the unit circle and for multi-orthogonal polynomials in which the measures involved are of the type described above.