Zobrazeno 1 - 10
of 189
pro vyhledávání: '"Nikolov, Geno"'
Autor:
Nikolov, Geno
Some new bounds for the extreme zeroes of Jacobi polynomials are obtained with an elementary approach. A feature of these bounds is their simple forms, which make them easy to work with. Despite their simplicity, our lower bounds for the largest zero
Externí odkaz:
http://arxiv.org/abs/2406.00849
Autor:
Nikolov, Geno, Nikolov, Petar
We study two modifications of the trapezoidal product cubature formulae, approximating double integrals over the square domain $[a,b]^2=[a,b]\times [a,b]$. Our modified cubature formulae use mixed type data: except evaluations of the integrand on the
Externí odkaz:
http://arxiv.org/abs/2404.17796
Autor:
Naidenov, Nikola, Nikolov, Geno
Here we study the quantity $$ \tau_{n,k}:=\frac{|T_n^{(k)}(\omega_{n,k})|}{T_n^{(k)}(1)}\,, $$ where $T_n$ is the $n$-th Chebyshev polynomial of the first kind and $\omega_{n,k}$ is the largest zero of $T_n^{(k+1)}$. Since the absolute values of the
Externí odkaz:
http://arxiv.org/abs/2203.05432
We study the behaviour of the smallest possible constants $d_n$ and $c_n$ in Hardy's inequalities $$ \sum_{k=1}^{n}\Big(\frac{1}{k}\sum_{j=1}^{k}a_j\Big)^2\leq d_n\,\sum_{k=1}^{n}a_k^2, \qquad (a_1,\ldots,a_n) \in \mathbb{R}^n $$ and $$ \int_{0}^{\in
Externí odkaz:
http://arxiv.org/abs/2007.10073
Autor:
Dimitrov, Dimitar K., Nikolov, Geno P.
For parameters $\,c\in(0,1)\,$ and $\,\beta>0$, let $\,\ell_{2}(c,\beta)\,$ be the Hilbert space of real functions defined on $\,\mathbb{N}\,$ (i.e., real sequences), for which $$ \| f \|_{c,\beta}^2 := \sum_{k=0}^{\infty}\frac{(\beta)_k}{k!}\,c^k\,[
Externí odkaz:
http://arxiv.org/abs/2007.04061
Autor:
Nikolov, Geno
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 particular, we derive upper and lower bound for $1-x_{nn}^2(\lambda)$, with $
Externí odkaz:
http://arxiv.org/abs/2002.02633
Autor:
Nikolov, Geno
We present a short proof that the normalized Tur\'{a}n determinant in the ultraspherical case is convex or concave depending on whether parameter $\lambda$ is positive or negative.
Comment: 6 pages
Comment: 6 pages
Externí odkaz:
http://arxiv.org/abs/2002.01393
Autor:
Nikolov, Geno
Askey and Gasper (1976) proved a trigonometric inequality which improves another trigonometric inequality found by M. S. Robertson (1945). Here these inequalities are reformulated in terms of the Chebyshev polynomial of the first kind $T_n$ and then
Externí odkaz:
http://arxiv.org/abs/2001.07013
Estimates for the best constant in a Markov $L_2$-inequality with the assistance of computer algebra
Autor:
Nikolov, Geno, Uluchev, Rumen
We prove two-sided estimates for the best (i.e., the smallest possible) constant $\,c_n(\alpha)\,$ in the Markov inequality $$ \|p_n'\|_{w_\alpha} \le c_n(\alpha) \|p_n\|_{w_\alpha}\,, \qquad p_n \in {\cal P}_n\,. $$ Here, ${\cal P}_n$ stands for the
Externí odkaz:
http://arxiv.org/abs/1711.07398