scholarly journals Zero location and asymptotic behavior for extremal polynomials with non-diagonal Sobolev norms

2010 ◽  
Vol 162 (12) ◽  
pp. 2225-2242 ◽  
Author(s):  
Ana Portilla ◽  
Yamilet Quintana ◽  
José M. Rodríguez ◽  
Eva Tourís
Keyword(s):  
Asymptotic Behavior ◽  
Extremal Polynomials ◽  
Sobolev Norms ◽  
Zero Location

scholarly journals Concerning Asymptotic Behavior for Extremal Polynomials Associated to Nondiagonal Sobolev Norms

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Ana Portilla ◽  
Yamilet Quintana ◽  
José M. Rodríguez ◽  
Eva Tourís
Keyword(s):  
Asymptotic Behavior ◽  
Admissible Pair ◽  
Sobolev Norm ◽  
Diagonal Matrix ◽  
Extremal Polynomials ◽  
Sobolev Norms ◽  
The Matrix ◽  
Complex Coefficients ◽  
Zero Location

Let ℙ be the space of polynomials with complex coefficients endowed with a nondiagonal Sobolev norm∥ · ∥W1,p(Vμ), where the matrixVand the measureμconstitute ap-admissible pair for1≤p≤∞. In this paper we establish the zero location and asymptotic behavior of extremal polynomials associated to∥ · ∥W1,p(Vμ), stating hypothesis on the matrixVrather than on the diagonal matrix appearing in its unitary factorization.

scholarly journals The Multiplication Operator, Zero Location and Asymptotic for Non-diagonal Sobolev Norms

2009 ◽  
Vol 111 (2) ◽  
pp. 205-218 ◽  
Author(s):  
Ana Portilla ◽  
José M. Rodríguez ◽  
Eva Tourís
Keyword(s):  
Multiplication Operator ◽  
Sobolev Norms ◽  
Zero Location

scholarly journals Asymptotic zero distribution for a class of extremal polynomials

2020 ◽  
pp. 1950019 ◽  
Author(s):  
A. Díaz González ◽  
G. López Lagomasino ◽  
H. Pijeira Cabrera
Keyword(s):  
Asymptotic Behavior ◽  
Convex Hull ◽  
Wide Class ◽  
Real Line ◽  
Sobolev Type ◽  
Point Distribution ◽  
The Real ◽  
Singular Measures ◽  
Extremal Polynomials ◽  
Asymptotic Zero Distribution

We consider extremal polynomials with respect to a Sobolev-type [Formula: see text]-norm, with [Formula: see text] and measures supported on compact subsets of the real line. For a wide class of such extremal polynomials with respect to mutually singular measures (i.e. supported on disjoint subsets of the real line), it is proved that their critical points are simple and contained in the interior of the convex hull of the support of the measures involved and the asymptotic critical point distribution is studied. We also find the [Formula: see text]th root asymptotic behavior of the corresponding sequence of Sobolev extremal polynomials and their derivatives.

scholarly journals Strong asymptotics forLpextremal polynomials off a complex curve

2004 ◽  
Vol 2004 (5) ◽  
pp. 371-378 ◽  
Author(s):  
Rabah Khaldi
Keyword(s):  
Asymptotic Behavior ◽  
Complex Plane ◽  
Jordan Curve ◽  
Infinite Number ◽  
Discrete Measure ◽  
Strong Asymptotics ◽  
Complex Curve ◽  
Extremal Polynomials

We study the asymptotic behavior ofLp(σ)extremal polynomials with respect to a measure of the formσ=α+γ, whereαis a measure concentrated on a rectifiable Jordan curve in the complex plane andγis a discrete measure concentrated on an infinite number of mass points.

Sign in / Sign up

Export Citation Format

Share Document