On Vladimir Markov type inequality in Lp norms on the interval [-1; 1]

2019 ◽  
Vol 7 (4) ◽  
pp. 9-12
Author(s):  
Mirosław Baran ◽  
Paweł Ozorka
Keyword(s):  
Linear Operator ◽  
Type Inequality ◽  
Normed Spaces ◽  
Markov Type ◽  
Lp Norms ◽  
Wiener Type

We prove inequality ||P(k)||Lp(-1;1)≤Bp||Tn(k)||Lp(-1;1)n^(2/p) ||P||Lp(-1;1); where Bp are constants independent of n = deg P with 1 ≤ p ≤ 2, which is sharp in the case k ≥ 3. A method presented in this note is based on a factorization of linear operator of k-th derivative throughout normed spaces of polynomial equipped with a Wiener type norm.

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.

A V. A. Markov type inequality in Lp

1983 ◽  
Vol 22 (2) ◽  
pp. 1226-1231
Author(s):  
A. N. Podkorytov ◽  
E. M. Dyn'kin
Keyword(s):  
Type Inequality ◽  
Markov Type

Inequalities for Rational Functions With Prescribed Poles

1998 ◽  
Vol 50 (1) ◽  
pp. 152-166 ◽  
Author(s):  
G. Min
Keyword(s):  
Type Inequality ◽  
Rational Functions ◽  
Complex Conjugation ◽  
Bernstein Type ◽  
Rational System ◽  
Markov Type ◽  
Classical Polynomials ◽  
Bernstein Type Inequalities

AbstractThis paper considers the rational system Pn(a1, a2,……,an) := with nonreal elements in paired by complex conjugation. It gives a sharp (to constant) Markov-type inequality for real rational functions in Pn(a1, a2,……an). The corresponding Markov-type inequality for high derivatives is established, as well as Nikolskii-type inequalities. Some sharp Markov- and Bernstein-type inequalities with curved majorants for rational functions in Pn(a1, a2,……an) are obtained, which generalize some results for the classical polynomials. A sharp Schur-type inequality is also proved and plays a key role in the proofs of our main results

A Markov-type inequality for seminormed fuzzy integrals

2013 ◽  
Vol 219 (22) ◽  
pp. 10746-10752 ◽  
Author(s):  
J. Caballero ◽  
K. Sadarangani
Keyword(s):  
Type Inequality ◽  
Markov Type

scholarly journals A formula to calculate the spectral radius of a compact linear operator

1997 ◽  
Vol 20 (3) ◽  
pp. 585-588 ◽  
Author(s):  
Fernando Garibay Bonales ◽  
Rigoberto Vera Mendoza
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Vector Space ◽  
Compact Operator ◽  
Spectral Radius ◽  
Topological Vector Space ◽  
Closed Subspace ◽  
Minkowski Functional ◽  
Normed Spaces ◽  
Locally Convex

There is a formula (Gelfand's formula) to find the spectral radius of a linear operator defined on a Banach space. That formula does not apply even in normed spaces which are not complete. In this paper we show a formula to find the spectral radius of any linear and compact operatorTdefined on a complete topological vector space, locally convex. We also show an easy way to find a non-trivialT-invariant closed subspace in terms of Minkowski functional.

scholarly journals Some Properties of Spectral Theory in Fuzzy Hilbert Spaces

2017 ◽  
Vol 8 (2) ◽  
pp. 1-7
Author(s):  
Noori F. Al-Mayahi ◽  
Abbas M. Abbas
Keyword(s):  
Linear Operator ◽  
Spectral Theory ◽  
Hilbert Spaces ◽  
Normed Spaces

In this paper we give some definitions and properties of spectral theory in fuzzy Hilbert spaces also we introduce  definitions Invariant  under a linear operator  on fuzzy normed spaces and reduced  linear operator on fuzzy Hilbert spaces and we prove theorms  related to eigenvalue and eigenvectors ,eigenspace in fuzzy normed , Invariant and  reduced in fuzzy Hilbert spaces  and  show relationship between them.

scholarly journals Invertible Operators on Soft Normed Spaces

2020 ◽  
pp. 1089-1097
Author(s):  
Sabah Aboud ◽  
Buthaina Abdul Hassan
Keyword(s):  
Linear Operator ◽  
Invertible Operator ◽  
Normed Spaces ◽  
Linear Spaces ◽  
New Concepts

Despite ample research on soft linear spaces, there are many other concepts that can be studied. We introduced in this paper several new concepts related to the soft operators, such as the invertible operator.  We investigated some properties of this kind of operators and defined the spectrum of soft linear operator along with a number of concepts related with this definition; the concepts of eigenvalue, eigenvector, eigenspace are defined. Finally the spectrum of the soft linear operator was divided into three disjoint parts.

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