scholarly journals The upper and lower quantization coefficient for Markov-type measures

2017 ◽  
Vol 290 (5-6) ◽  
pp. 827-839
Author(s):  
Marc Kesseböhmer ◽  
Sanguo Zhu
Keyword(s):  
Markov Type ◽  
Quantization Coefficient

Bernstein and Markov Type Inequalities for Generalized Non-Negative Polynomials

1991 ◽  
Vol 43 (3) ◽  
pp. 495-505 ◽  
Author(s):  
Tamás Erdélyi
Keyword(s):  
Absolute Constant ◽  
Positive Real ◽  
Generalized Polynomials ◽  
Markov Type ◽  
Natural Way

AbstractGeneralized polynomials are defined as products of polynomials raised to positive real powers. The generalized degree can be introduced in a natural way. Several inequalities holding for ordinary polynomials are expected to be true for generalized polynomials, by utilizing the generalized degree in place of the ordinary one. Based on Remez-type inequalities on the size of generalized polynomials, we establish Bernstein and Markov type inequalities for generalized non-negative polynomials, obtaining the best possible result up to a multiplicative absolute constant.

scholarly journals Alexander- and Markov-type theorems for virtual trivalent braids

2019 ◽  
Vol 28 (01) ◽  
pp. 1950003 ◽  
Author(s):  
Carmen Caprau ◽  
Abigayle Dirdak ◽  
Rita Post ◽  
Erica Sawyer
Keyword(s):  
Type Theorem ◽  
Algebraic Approach ◽  
The Other ◽  
Markov Type ◽  
Trivalent Graphs

We prove Alexander- and Markov-type theorems for virtual spatial trivalent graphs and virtual trivalent braids. We provide two versions for the Markov-type theorem: one uses an algebraic approach similar to the case of classical braids and the other one is based on [Formula: see text]-moves.

scholarly journals Lupaş-type inequality and applications to Markov-type inequalities in weighted Sobolev spaces

2020 ◽  
pp. 1950022
Author(s):  
Francisco Marcellán ◽  
José M. Rodríguez
Keyword(s):  
Sobolev Spaces ◽  
Jacobi Polynomials ◽  
Weighted Sobolev Spaces ◽  
Type Inequality ◽  
The Other ◽  
Main Role ◽  
Markov Type ◽  
Sobolev Orthogonal Polynomials ◽  
Approximation Problems ◽  
Connection Formulas

Weighted Sobolev spaces play a main role in the study of Sobolev orthogonal polynomials. In particular, analytic properties of such polynomials have been extensively studied, mainly focused on their asymptotic behavior and the location of their zeros. On the other hand, the behavior of the Fourier–Sobolev projector allows to deal with very interesting approximation problems. The aim of this paper is twofold. First, we improve a well-known inequality by Lupaş by using connection formulas for Jacobi polynomials with different parameters. In the next step, we deduce Markov-type inequalities in weighted Sobolev spaces associated with generalized Laguerre and generalized Hermite weights.

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