G. Nikolov

activity

20122022

L_{2}

-inequality with the Laguerre weight

3 citations · 6 across the 12 of their papers we have counts for

collaborators

15 papers

math.CA2022

Estimates for the largest critical value of $T_{n}^{(k)}$

Nikola Naidenov, Geno Nikolov

Here we study the quantity $τ_{n, k} := \frac{∣ T _{n}^{(k)} ( ω _{n, k} ) ∣}{T _{n}^{(k)} ( 1 )},$ where $T_{n}$ is the $n$ -th Chebyshev polynomial of the first kind and $ω_{n, k}$ is the largest…

math.CA2020

Hardy's inequalities in finite dimensional Hilbert spaces

Dimitar K. Dimitrov, Ivan Gadjev, Geno Nikolov +1

We study the behaviour of the smallest possible constants $d_{n}$ and $c_{n}$ in Hardy's inequalities $$ \sum_{k=1}^{n}\Big(\frac{1}{k}\sum_{j=1}^{k}a_j\Big)^2\leq d_n\,\sum_{k=1}^{n}a…

math.CA2020

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

Dimitar K. Dimitrov, Geno P. Nikolov

For parameters $c \in (0, 1)$ and $β > 0$ , let $ℓ_{2} (c, β)$ be the Hilbert space of real functions defined on $N$ (i.e., real sequences), for which $$ \| f \|_…

math.CA2020

On the extreme zeros of Jacobi polynomials

Geno Nikolov

By applying the Euler--Rayleigh methods to a specific representation of the Jacobi polynomials as hypergeometric functions, we obtain new bounds for their largest zeros. In particu…

math.CA2020

Turán's inequality for ultraspherical polynomials revisited

Geno Nikolov

We present a short proof that the normalized Turán determinant in the ultraspherical case is convex or concave depending on whether parameter $λ$ is positive or negative.

math.CA2020

Some inequalities for Chebyshev polynomials

Geno Nikolov

Askey and Gasper (1976) proved a trigonometric inequality which improves another trigonometric inequality found by M. S. Robertson (1945). Here these inequalities are reformulated…

math.CA2017★ 1 cited

Estimates for the best constant in a Markov $L_{2}$ -inequality with the assistance of computer algebra

Geno Nikolov, Rumen Uluchev

We prove two-sided estimates for the best (i.e., the smallest possible) constant $c_{n} (α)$ in the Markov inequality $$ \|p_n'\|_{w_α} \le c_n(α) \|p_n\|_{w_α}\,, \qquad p_n \in…

math.CA2017

On the largest critical value of $T_{n}^{(k)}$

Geno Nikolov, Nikola Naidenov, Alexei Shadrin

We study the quantity $τ_{n, k} := \frac{∣ T _{n}^{(k)} ( ω _{n, k} ) ∣}{T _{n}^{(k)} ( 1 )},$ where $T_{n}$ is the Chebyshev polynomial of degree $n$ , and $ω_{n, k}$ is the rightmost zero of $T_n…

math.CA2017★ 3 cited

Markov $L_{2}$ -inequality with the Laguerre weight

Geno Nikolov, Alexei Shadrin

Let $w_{α} (t) := t^{α} e^{- t}$ , where $α > - 1$ , be the Laguerre weight function, and let $∥ \cdot ∥_{w_{α}}$ be the associated $L_{2}$ -norm, $$ \|f\|_{w_α} = \left\{\int_{0}^{\infty} |f(x)…

math.CA2017

Markov $L_{2}$ inequality with the Gegenbauer weight

Dragomir Aleksov, Geno Nikolov

For the Gegenbauer weight function $w_{λ} (t) = (1 - t^{2})^{λ - 1/2}$ , $λ > - 1/2$ , we denote by $∥ \cdot ∥_{w_{λ}}$ the associated $L_{2}$ -norm, $$ \Vert f\Vert_{w_λ}:=\Big(\int_{-1}^{1}w_λ(…

math.CA2017

On the Markov inequality in the $L_{2}$ -norm with the Gegenbauer weight

Geno Nikolov, Alexei Shadrin

Let $w_{λ} (t) := (1 - t^{2})^{λ - 1/2}$ , where $λ > - \frac{1}{2}$ , be the Gegenbauer weight function, let $∥ \cdot ∥_{w_{λ}}$ be the associated $L_{2}$ -norm, $$ \|f\|_{w_λ} = \left\{\int_{-1}^1…

math.NA2016

Asymptotically optimal definite quadrature formulae of $4$ -th order

Ana Avdzhieva, Geno Nikolov

We construct several sequences of asymptotically optimal definite quadrature formulae of fourth order and evaluate their error constants. Besides the asymptotical optimality, an ad…

math.CA2016

On the $L_{2}$ Markov Inequality with Laguerre Weight

Geno Nikolov, Alexei Shadrin

Let $w_{α} (t) = t^{α} e^{- t}$ , $α > - 1$ , be the Laguerre weight function, and $∣ \cdot ∣_{w_{α}}$ denote the associated $L_{2}$ -norm, i.e., $$ | f|_{w_α}:=\Big(\int_{0}^{\infty}w_α(t)| f(t)|^2\…

math.CA2014

Inequalities for ultraspherical polynomials. Proof of a conjecture of I. Raşa

Geno Nikolov

A recent conjecture by I. Raşa asserts that the sum of the squared Bernstein basis polynomials is a convex function in $[0, 1]$ . This conjecture turns out to be equivalent to a cert…

math.NA2012★ 2 cited

On Markov-Duffin-Schaeffer inequalities with a majorant. II

Geno Nikolov, Alexei Shadrin

We are continuing out studies of the so-called Markov inequalities with a majorant. Inequalities of this type provide a bound for the $k$ -th derivative of an algebraic polynomial w…

Estimates for the largest critical value of Tn(k)​

Hardy's inequalities in finite dimensional Hilbert spaces

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

On the extreme zeros of Jacobi polynomials

Turán's inequality for ultraspherical polynomials revisited

Some inequalities for Chebyshev polynomials

Estimates for the best constant in a Markov L2​-inequality with the assistance of computer algebra

On the largest critical value of Tn(k)​

Markov L2​-inequality with the Laguerre weight

Markov L2​ inequality with the Gegenbauer weight

On the Markov inequality in the L2​-norm with the Gegenbauer weight

Asymptotically optimal definite quadrature formulae of 4-th order

On the L2​ Markov Inequality with Laguerre Weight

Inequalities for ultraspherical polynomials. Proof of a conjecture of I. Raşa

On Markov-Duffin-Schaeffer inequalities with a majorant. II

Estimates for the largest critical value of $T_{n}^{(k)}$

Estimates for the best constant in a Markov $L_{2}$ -inequality with the assistance of computer algebra

On the largest critical value of $T_{n}^{(k)}$

Markov $L_{2}$ -inequality with the Laguerre weight

Markov $L_{2}$ inequality with the Gegenbauer weight

On the Markov inequality in the $L_{2}$ -norm with the Gegenbauer weight

Asymptotically optimal definite quadrature formulae of $4$ -th order

On the $L_{2}$ Markov Inequality with Laguerre Weight