dc.contributor.author |
Tikhonov, S. |
dc.contributor.author |
Yuditskii, P. |
dc.date.accessioned |
2020-11-27T08:37:55Z |
dc.date.available |
2020-11-27T08:37:55Z |
dc.date.issued |
2019-07-01 |
dc.identifier.uri |
http://hdl.handle.net/2072/378031 |
dc.format.extent |
14 p. |
dc.language.iso |
eng |
dc.relation.ispartof |
Constructive Approximation (Springer) |
dc.rights |
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons:http://creativecommons.org/licenses/by-nc-nd/4.0/ |
dc.source |
RECERCAT (Dipòsit de la Recerca de Catalunya) |
dc.subject.other |
Matemàtiques |
dc.title |
Sharp Remez Inequality |
dc.type |
info:eu-repo/semantics/article |
dc.type |
info:eu-repo/semantics/draft |
dc.subject.udc |
51 - Matemàtiques |
dc.embargo.terms |
cap |
dc.identifier.doi |
10.1007/s00365-019-09473-2 |
dc.rights.accessLevel |
info:eu-repo/semantics/openAccess |
dc.description.abstract |
Let an algebraic polynomial $$P_n(\zeta )$$Pn(ζ)of degree n be such that $$|P_n(\zeta )|\leqslant 1$$|Pn(ζ)|⩽1for $$\zeta \in E\subset \mathbb {T}$$ζ∈E⊂Tand $$|E|\geqslant 2\pi -s$$|E|⩾2π-s. We prove the sharp Remez inequality $$\begin{aligned} \sup _{\zeta \in \mathbb {T}}|P_n(\zeta )|\leqslant {\mathfrak {T}}_{n}\left( \sec \frac{s}{4}\right) , \end{aligned}$$supζ∈T|Pn(ζ)|⩽Tnsecs4,where $${\mathfrak {T}}_{n}$$Tnis the Chebyshev polynomial of degree n. The equality holds if and only if $$\begin{aligned} P_n(e^{iz})=e^{i(nz/2+c_1)}{\mathfrak {T}}_n\left( \sec \frac{s}{4}\cos \frac{z-c_0}{2}\right) , \quad c_0,c_1\in {\mathbb {R}}. \end{aligned}$$Pn(eiz)=ei(nz/2+c1)Tnsecs4cosz-c02,c0,c1∈R.This gives the solution of the long-standing problem on the sharp constant in the Remez inequality for trigonometric polynomials. |