Published April 2017
| Submitted
Journal Article
Open
Asymptotics of Chebyshev polynomials, I: subsets of ℝ
Abstract
We consider Chebyshev polynomials, T_n(z), for infinite, compact sets e⊂ℝ (that is, the monic polynomials minimizing the sup-norm, ||T_n||_e, on e). We resolve a 45+ year old conjecture of Widom that for finite gap subsets of R, his conjectured asymptotics (which we call Szegő–Widom asymptotics) holds. We also prove the first upper bounds of the form ||T_n||_e≤QC(e)^n(where C(e) is the logarithmic capacity of e) for a class of e's with an infinite number of components, explicitly for those e⊂ℝ that obey a Parreau–Widom condition.
Additional Information
© 2016 Springer-Verlag Berlin Heidelberg. Received: 18 October 2015; Accepted: 30 April 2016; First Online: 19 September 2016. B. Simon's research was supported in part by NSF Grant DMS-1265592 and in part by Israeli BSF Grant No. 2010348. M. Zinchenko's research was supported in part by Simons Foundation Grant CGM-281971.Attached Files
Submitted - 1505.02604v1.pdf
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Additional details
- Eprint ID
- 71891
- Resolver ID
- CaltechAUTHORS:20161109-142515049
- DMS-1265592
- NSF
- 2010348
- Binational Science Foundation (USA-Israel)
- CGM-281971
- Simons Foundation
- Created
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2016-11-09Created from EPrint's datestamp field
- Updated
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2021-11-11Created from EPrint's last_modified field