Access the full text.
Sign up today, get DeepDyve free for 14 days.
P A Borodin (1997)
On polynomials most divergent from zero on a domain boundaryMoscow University Mathematics Bulletin, 52
G Faber (1919)
Über Tschebyscheffsche PolynomeJ. für Math., 150
M. Götz, E. Saff (2000)
Potential and Discrepancy Estimates for Weighted Extremal PointsConstructive Approximation, 16
V. Andrievskii, H. Blatt (2001)
Discrepancy of Signed Measures and Polynomial Approximation
Björn Gustafsson (1998)
On mother bodies of convex poyhedraSiam Journal on Mathematical Analysis, 29
Björn Gustafsson (1997)
Direct and inverse balayage — Some new developments in classical potential theoryNonlinear Analysis-theory Methods & Applications, 30
E. Saff, V. Totik (1997)
Logarithmic Potentials with External Fields
For a bounded domain G in the complex plane, we focus on the problem of maximizing the minimum on the boundary ∂G of (weighted) polynomials of degree n having all zeros in a set D ⊂ G. For arbitrary unit measures μ on ∂ G and weight w:= exp{Uμ}, the n-th root asymptotics of \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\matrix{{\rm sup} \cr pn} \matrix{{\rm inf} \cr z \varepsilon \partial G} \mid P_n(z)\omega^n(z) \mid$$\end{document} is considered and related to the existence and construction of an inverse balayage of μ on \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\overline D$$\end{document}, i.e. of a measure such that μ is its balayage when sweeping to ∂G.
Computational Methods and Function Theory – Springer Journals
Published: Aug 1, 2005
Keywords: Logarithmic potential; weighted polynomial; equilibrium distribution; capacity; balayage; inverse balayage; 31A15; 30C85; 41A17
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.