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of 159
pro vyhledávání: '"Dimitrov, Dimitar K."'
We study the behavior of the smallest possible constants $d(a,b)$ and $d_n$ in Hardy's inequalities $$ \int_a^b\left(\frac{1}{x}\int_a^xf(t)dt\right)^2\,dx\leq d(a,b)\,\int_a^b [f(x)]^2 dx $$ and $$ \sum_{k=1}^{n}\Big(\frac{1}{k}\sum_{j=1}^{k}a_j\Big
Externí odkaz:
http://arxiv.org/abs/2306.08172
We study two variations of the classical one-delta problem for entire functions of exponential type, known also as the Carath\'eodory--Fej\'er--Tur\'an problem. The first variation imposes the additional requirement that the function is radially decr
Externí odkaz:
http://arxiv.org/abs/2304.05337
Autor:
Dimitrov, Dimitar K., Lun, Yen Chi
Publikováno v:
In Journal of Approximation Theory January 2025 305
We study the behaviour of the smallest possible constants $d_n$ and $c_n$ in Hardy's inequalities $$ \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:
Dimitrov, Dimitar K., Shapiro, Boris
In this note we extend the classical relation between the equilibrium configurations of unit movable point charges in a plane electrostatic field created by these charges together with some fixed point charges and the polynomial solutions of a corres
Externí odkaz:
http://arxiv.org/abs/1806.02962
Akademický článek
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We establish generalizations of the Nyman-Beurling and B\'aez-Duarte criteria concerning lack of zeros of Dirichlet $L$-functions in the semi-plane $\Re(s) >1/p$ for $p\in (1,2]$. We pose and solve a natural extremal problem for Dirichlet polynomials
Externí odkaz:
http://arxiv.org/abs/1608.07887
Autor:
Dimitrov, Dimitar K., Xu, Yuan
Associated with a given suitable function, or a measure, on $\mathbb{R}$, we introduce a correlation function, so that the Wronskian of the Fourier transform of the function is the Fourier transform of the corresponding correlation function, and the
Externí odkaz:
http://arxiv.org/abs/1606.05011
We prove that the signs of the Maclaurin coefficients of a wide class of entire functions that belong to the Laguerre-P\'olya class posses a regular behaviour.
Comment: 12 pages
Comment: 12 pages
Externí odkaz:
http://arxiv.org/abs/1601.05487