Gardado en:
| Autor Principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Subjects: | |
| Acceso en liña: | https://arxiv.org/abs/2412.18656 |
| Tags: |
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Table of Contents:
- We consider the asymptotics of orthogonal polynomials for measures that are differentiable, but not necessarily analytic, multiplicative perturbations of Jacobi-like measures supported on disjoint intervals. We analyze the Fokas-Its-Kitaev Riemann-Hilbert problem using the Deift-Zhou method of nonlinear steepest descent and its $\overline{\partial}$ extension due to Miller and McLaughlin. Our results extend that of Yattselev in the case of Chebyshev-like measures with error bounds that give similar rates while allowing less regular perturbations. For the general Jacobi-like case, we present, what appears to be the first result for asymptotics when the perturbation of the measure is only assumed to be differentiable with bounded second derivative.