The smallest eigenvalue of large Hankel matrices associated with a singularly perturbed Gaussian weight
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- by Dan Wang, Mengkun Zhu and Yang Chen PDF
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Abstract:
An asymptotic expression for the polynomials $\mathcal {P}_n(z)$, $z\notin (-\infty ,\infty )$, orthonormal with respect to a singularly perturbed Gaussian weight, $\exp (-z^2-t/z^2),~z\in (-\infty ,\infty ),~t>0$, is established. Based on this, the asymptotic behavior of the smallest eigenvalue of the Hankel matrix generated by the weight is described.References
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Additional Information
- Dan Wang
- Affiliation: Department of Applied Mathematics, School of Computer Science and Artificial Intelligence, Changzhou University 213164, People’s Republic of China
- ORCID: 0000-0002-8709-1974
- Email: bohewan@126.com
- Mengkun Zhu
- Affiliation: School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences) Jinan 250353, People’s Republic of China; and Department of Mathematics, Faculty of Science and Technology, University of Macau, Avenida da Universidade, Taipa, Macau, People’s Republic of China
- ORCID: 0000-0002-2214-7025
- Email: zmk@qlu.edu.cn; and Zhu_mengkun@163.com
- Yang Chen
- Affiliation: Department of Mathematics, Faculty of Science and Technology, University of Macau, Avenida da Universidade, Taipa, Macau, People’s Republic of China
- Email: yayangchen@um.edu.mo
- Received by editor(s): January 14, 2021
- Received by editor(s) in revised form: June 16, 2021
- Published electronically: October 25, 2021
- Additional Notes: The second author was supported by the Natural Science Foundation of Shandong Province under Grant no. ZR202102270243.
The second author and the third author was supported by the Natural Science Foundation of Guangdong Province under Grant no. 2021A1515010361.
The second author is the corresponding author - Communicated by: Mourad Ismail
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 153-160
- MSC (2020): Primary 15B57, 42C05, 65R10
- DOI: https://doi.org/10.1090/proc/15757
- MathSciNet review: 4335865