2 citations · 11 across the 27 of their papers we have counts for
18 papers · 1 filter
Extremal problems for polynomials with real roots
Arturas Dubickas, Igor Pritsker
We consider polynomials of degree with only real roots and a fixed value of discriminant, and study the problem of minimizing the absolute value of polynomials at a fixed point…
Weighted Fekete points on the real line and the unit circle
Arturas Dubickas, Igor Pritsker
Weighted Fekete points are defined as those that maximize the weighted version of the Vandermonde determinant over a fixed set. They can also be viewed as the equilibrium distribut…
Random Bernstein-Markov factors
Igor Pritsker, Koushik Ramachandran
For a polynomial of degree , Bernstein's inequality states that for all norms on the unit circle, with equality for $P_n(z)=…
Equidistribution of zeros of random polynomials
Igor Pritsker, Koushik Ramachandran
We study the asymptotic distribution of zeros for the random polynomials , where are non-trivial i.i.d. complex random va…
Expected discrepancy for zeros of random algebraic polynomials
Igor E. Pritsker, Alan A. Sola
We study asymptotic clustering of zeros of random polynomials, and show that the expected discrepancy of roots of a polynomial of degree , with not necessarily independent coeff…
Inequalities for sums of Green potentials and Blaschke products
Igor E. Pritsker
We study inequalities for the infima of Green potentials on a compact subset of an arbitrary domain in the complex plane. The results are based on a new representation of the pseud…
Equidistribution of points via energy
Igor E. Pritsker
We study the asymptotic equidistribution of points with discrete energy close to Robin's constant of a compact set in the plane. Our main tools are the energy estimates from potent…
Reverse Triangle Inequalities for Potentials
I. E. Pritsker, E. B. Saff
We study the reverse triangle inequalities for suprema of logarithmic potentials on compact sets of the plane. This research is motivated by the inequalities for products of suprem…
Convergence of Julia polynomials
Igor E. Pritsker
We study the approximation of conformal mappings with the polynomials defined by Keldysh and Lavrentiev from an extremal problem considered by Julia. These polynomials converge uni…
How to find a measure from its potential
Igor E. Pritsker
We consider the problem of finding a measure from the given values of its logarithmic potential on the support. It is well known that a solution to this problem is given by the gen…
Inequalities for products of polynomials I
I. E. Pritsker, S. Ruscheweyh
We study inequalities connecting the product of uniform norms of polynomials with the norm of their product. This circle of problems include the Gelfond-Mahler inequality for the u…
Weighted energy problem on the unit circle
Igor E. Pritsker
We solve the weighted energy problem on the unit circle, by finding the extremal measure and describing its support. Applications to polynomial and exponential weights are also inc…
Approximation of conformal mapping via the Szegő kernel method
Igor E. Pritsker
We study the uniform approximation of the canonical conformal mapping, for a Jordan domain onto the unit disk, by polynomials generated from the partial sums of the Szegő kernel ex…
Moment inequalities for equilibrium measures in the plane
A. Baernstein, R. S. Laugesen, I. E. Pritsker
The equilibrium measure of a compact plane set gives the steady state distribution of charges on the conductor. We show that certain moments of this equilibrium measure, when taken…
Norms of products and factors polynomials
Igor E. Pritsker
We study inequalities connecting a product of uniform norms of polynomials with the norm of their product. Generalizing Gel'fond-Mahler inequality for the unit disk and Kneser-Borw…
Simultaneous approximation and interpolation of functions on continua in the complex plane
V. V. Andrievskii, I. E. Pritsker, R. S. Varga
We construct polynomial approximations of Dzjadyk type (in terms of the k-th modulus of continuity, ) for analytic functions defined on a continuum E in the complex plane,…
On zeros of polynomials orthogonal over a convex domain
V. V. Andrievskii, I. E. Pritsker, R. S. Varga
We establish a discrepancy theorem for signed measures, with a given positive part, which are supported on an arbitrary convex curve. As a main application, we obtain a result conc…
An inequality for the norm of a polynomial factor
Igor E. Pritsker
Let be a monic polynomial of degree , with complex coefficients, and let be its monic factor. We prove an asymptotically sharp inequality of the form $\|q\|_{E} \l…