39 citations · 77 across the 12 of their papers we have counts for
14 papers
Weak and strong -analogs of the Laguerre--Pólya class
D. K. Dimitrov, B. Shapiro
For we compare two natural -analogs of the Laguerre--Pólya class. The first one is a coefficient-side class, defined as the inverse image of the classical Laguerre--Póly…
Sharp Hardy's Inequalities in Hilbert Spaces
Dimitar K. Dimitrov, Ivan Gadjev, Mourad E. H. Ismail
We study the behavior of the smallest possible constants and in Hardy's inequalities $$ \int_a^b\left(\frac{1}{x}\int_a^xf(t)dt\right)^2\,dx\leq d(a,b)\,\int_a^b [f(…
An extremal problem and inequalities for entire functions of exponential type
Andrés Chirre, Dimitar K. Dimitrov, Emily Quesada-Herrera +1
We study two variations of the classical one-delta problem for entire functions of exponential type, known also as the Carathéodory--Fejér--Turán problem. The first variation impos…
Hardy's inequalities in finite dimensional Hilbert spaces
Dimitar K. Dimitrov, Ivan Gadjev, Geno Nikolov +1
We study the behaviour of the smallest possible constants and in Hardy's inequalities $$ \sum_{k=1}^{n}\Big(\frac{1}{k}\sum_{j=1}^{k}a_j\Big)^2\leq d_n\,\sum_{k=1}^{n}a…
A discrete weighted Markov--Bernstein inequality for polynomials and sequences
Dimitar K. Dimitrov, Geno P. Nikolov
For parameters and , let be the Hilbert space of real functions defined on (i.e., real sequences), for which $$ \| f \|_…
Electrostatic problems with a rational constraint and degenerate Lame equations
Dimitar K. Dimitrov, Boris Shapiro
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…