Markov-type inequalities and extreme zeros of orthogonal polynomials

Nikolov, Geno; Shadrin, Alexei

doi:10.1016/j.jat.2021.105644

Cited by 5 publications

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A relation between the best Markov constants γ n , n ∈ N, and the smallest eigenvalues of some Jacobi matrices is established in Section 4. It is worth noticing that this result applies to more general situations, concerning the sharp constants in a wide class of polynomial inequalities in L 2 -norms (see [1,33]). In Section 5 we obtain two-sided estimates for γ n (c, 1) which complete the proof of Theorem 1.1 (i).…”

Section: Introduction and Statement Of The Resultsmentioning

confidence: 89%

A discrete weighted Markov--Bernstein inequality for polynomials and sequences

Dimitrov¹,

Nikolov²

2020

Preprint

View full text Add to dashboard Cite

For parameters c ∈ (0, 1) and β > 0, let ℓ 2 (c, β) be the Hilbert space of real functions defined on N (i.e., real sequences), for whichWe study the best (i.e., the smallest possible) constant γn(c, β) in the discrete Markov-Bernstein inequalitywhere Pn is the set of real algebraic polynomials of degree at most n and ∆f (x) := f (x + 1) − f (x) .We prove that(ii) For every fixed c ∈ (0, 1) , γn(c, β) is a monotonically decreasing function of β in (0, ∞) ; (iii) For every fixed c ∈ (0, 1) and β > 0 , the best Markov-Bernstein constants γn(c, β) are bounded uniformly with respect to n. A similar Markov-Bernstein unequality is proved for sequences in ℓ 2 (c, β) . We also establish a relation between the best Markov-Bernstein constants γn(c, β) and the smallest eigenvalues of certain explicitly given Jacobi matrices.

show abstract

Section: Introduction and Statement Of The Resultsmentioning

confidence: 89%

A discrete weighted Markov--Bernstein inequality for polynomials and sequences

Dimitrov¹,

Nikolov²

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Extremal polynomials -called 'snake polynomials' -equioscillate between these bounds [19]. For more on this we refer the reader, for example, to [9], [8], [20] and [23].…”

Section: § 1 Introductionmentioning

confidence: 99%

On the weighted Bojanov-Chebyshev problem and the sum of translates method of Fenton

Farkas,

Nagy,

Révész

2023

Sb. Math.

View full text Add to dashboard Cite

Minimax and maximin problems are investigated for a special class of functions on the interval $[0,1]$. These functions are sums of translates of positive multiples of one kernel function and a very general external field function. Due to our very general setting the minimax, equioscillation and characterization results obtained extend those of Bojanov, Fenton, Hardin, Kendall, Saff, Ambrus, Ball and Erdélyi. Moreover, we discover a surprising intertwining phenomenon of interval maxima, which provides new information even in the most classical extremal problem of Chebyshev. Bibliography: 25 titles.

show abstract

On the Extreme Zeros of Jacobi Polynomials

Nikolov

2023

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Markov-type inequalities and extreme zeros of orthogonal polynomials

Cited by 5 publications

References 7 publications

A discrete weighted Markov--Bernstein inequality for polynomials and sequences

A discrete weighted Markov--Bernstein inequality for polynomials and sequences

On the weighted Bojanov-Chebyshev problem and the sum of translates method of Fenton

On the Extreme Zeros of Jacobi Polynomials

Contact Info

Product

Resources

About