Zobrazeno 1 - 10
of 158
pro vyhledávání: '"Zinchenko, Maxim"'
Autor:
Alpan, Gökalp, Zinchenko, Maxim
We derive optimal asymptotic and non-asymptotic lower bounds on the Widom factors for weighted Chebyshev and orthogonal polynomials on compact subsets of the real line. In the Chebyshev case we extend the optimal non-asymptotic lower bound previously
Externí odkaz:
http://arxiv.org/abs/2408.11496
We survey results on Chebyshev polynomials centered around the work of H. Widom. In particular, we discuss asymptotics of the polynomials and their norms and general upper and lower bounds for the norms. Several open problems are also presented.
Externí odkaz:
http://arxiv.org/abs/2112.06450
We look at periodic Jacobi matrices on trees. We provide upper and lower bounds on the gap of such operators analogous to the well known gap in the spectrum of the Laplacian on the upper half-plane with hyperbolic metric. We make some conjectures abo
Externí odkaz:
http://arxiv.org/abs/2010.01701
We study residual polynomials, $R_{x_0,n}^{(\mathfrak{e})}$, $\mathfrak{e}\subset\mathbb{R}$, $x_0\in\mathbb{R}\setminus\mathfrak{e}$, which are the degree at most $n$ polynomials with $R(x_0)=1$ that minimize the $\sup$ norm on $\mathfrak{e}$. New a
Externí odkaz:
http://arxiv.org/abs/2008.09669
Autor:
Alpan, Gökalp, Zinchenko, Maxim
We continue our study of the Widom factors for $L_p(\mu)$ extremal polynomials initiated in [4]. In this work we characterize sets for which the lower bounds obtained in [4] are saturated, establish continuity of the Widom factors with respect to the
Externí odkaz:
http://arxiv.org/abs/2005.09114
Autor:
Gesztesy, Fritz, Zinchenko, Maxim
We revisit an archive submission by P. B. Denton, S. J. Parke, T. Tao, and X. Zhang, arXiv:1908.03795, on $n \times n$ self-adjoint matrices from the point of view of self-adjoint Dirichlet Schr\"odinger operators on a compact interval.
Comment:
Comment:
Externí odkaz:
http://arxiv.org/abs/2003.10383
Autor:
Alpan, Gökalp, Zinchenko, Maxim
We derive lower bounds for the $L^p(\mu)$ norms of monic extremal polynomials with respect to compactly supported probability measures $\mu$. We obtain a sharp universal lower bound for all $0
Externí odkaz:
http://arxiv.org/abs/1907.12492
We make a number of comments on Chebyshev polynomials for general compact subsets of the complex plane. We focus on two aspects: asymptotics of the zeros and explicit Totik--Widom upper bounds on their norms.
Externí odkaz:
http://arxiv.org/abs/1812.10667
We determine which sets saturate the Szeg}o and Schiefermayr lower bounds on the norms of Chebyshev Polynomials. We also discuss sets that saturate the Totik--Widom upper bound.
Comment: Intended for the book "Analysis as a Tool in Mathematical
Comment: Intended for the book "Analysis as a Tool in Mathematical
Externí odkaz:
http://arxiv.org/abs/1712.03482
Publikováno v:
Duke Math. J. 168, no. 2 (2019), 325-349
We prove Szeg\H{o}-Widom asymptotics for the Chebyshev polynomials of a compact subset of $\mathbb{R}$ which is regular for potential theory and obeys the Parreau-Widom and DCT conditions.
Externí odkaz:
http://arxiv.org/abs/1709.06707