12 citations · 37 across the 19 of their papers we have counts for
23 papers
Strong asymptotics for Jacobi-Piñeiro orthogonal polynomials
Sergei Kalmykov, Vladimir Lysov, Vinay Shukla
We investigate the asymptotic behavior of Jacobi-Piñeiro polynomials of degree orthogonal on with respect to weights , where $α_1,α_2,…
Evaluation of terminating and non-terminating sums containing the digamma function
Sergei Kalmykov, Dmitrii Karp, Vinay Shukla
We derive transformation and summation formulas for terminating and nonterminating series involving the digamma function. Our principal results are obtained by a limiting process s…
A sharp bound on the number of self-intersections of a trigonometric curve
Sergei Kalmykov, Leonid V. Kovalev
We obtain a sharp bound on the number of self-intersections of a closed planar curve with trigonometric parameterization. Moreover, we show that a generic curve of this form is nor…
Estimates of Lebesgue Constants for Lagrange Interpolation Processes by Rational Functions under Mild Restrictions to their Fixed Poles
Sergei Kalmykov, Alexey Lukashov
We estimate the Lebesgue constants for Lagrange interpolation processes on one or several intervals by rational functions with fixed poles. We admit that the poles have accumulatio…
Bernstein- and Markov-type inequalities
Sergei Kalmykov, Béla Nagy, Vilmos Totik
This survey discusses the classical Bernstein and Markov inequalities for the derivatives of polynomials, as well as some of their extensions to general sets.
Continuity of logarithmic capacity
Sergei Kalmykov, Leonid V. Kovalev
We prove the continuity of logarithmic capacity under Hausdorff convergence of uniformly perfect planar sets. The continuity holds when the Hausdorff distance to the limit set tend…
A new identity for the sum of products of generalized basic hypergeometric functions
S. I. Kalmykov, D. Karp, A. Kuznetsov
We prove a duality relation for generalized basic hypergeometric functions. It forms a -extension of a recent result of the second and the third named authors and generalizes bo…
Minimal degree rational open up mappings and related questions
Sergei Kalmykov, Béla Nagy, Olivier Sète
We establish the existence and uniqueness of rational conformal maps of minimal degree for opening up arcs. In earlier results, the degree was exponential in . We also…
Self-intersections of Laurent polynomials and the density of Jordan curves
Sergei Kalmykov, Leonid V. Kovalev
We extend Quine's bound on the number of self-intersection of curves with polynomial parameterization to the case of Laurent polynomials. As an application, we show that circle emb…
Inequalities for some basic hypergeometric functions
S. I. Kalmykov, D. B. Karp
We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric function with respect simultaneous shi…
New identities for a sum of products of the Kummer functions
S. I. Kalmykov, D. B. Karp
Recently, Feng, Kuznetsov and Yang discovered a very general reduction formula for a sum of products of the generalized hypergeometric functions (J. Math. Anal. Appl. 443(2016), 11…
Removable sets for intrinsic metric and for holomorphic functions
Sergei Kalmykov, Leonid V. Kovalev, Tapio Rajala
We study the subsets of metric spaces that are negligible for the infimal length of connecting curves; such sets are called metrically removable. In particular, we show that every…
Uniform convergence of Green's functions
Sergei Kalmykov, Leonid V. Kovalev
Given a sequence of regular planar domains converging in the sense of kernel, we prove that the corresponding Green's functions converge uniformly on the complex sphere, provided t…
Higher Markov and Bernstein inequalities and fast decreasing polynomials with prescribed zeros
Sergei Kalmykov, Béla Nagy
Higher order Bernstein- and Markov-type inequalities are established for trigonometric polynomials on compact subsets of the real line and algebraic polynomials on compact subsets…
Log-concavity and Turán-type inequalities for the generalized hypergeometric function
S. I. Kalmykov, D. B. Karp
The paper studies logarithmic convexity and concavity of the generalized hypergeometric function with respect to simultaneous shift of several parameters. We use integral represent…
Bernstein- and Markov-type inequalities for rational functions
Sergei Kalmykov, Béla Nagy, Vilmos Totik
Asymptotically sharp Bernstein- and Markov-type inequalities are established for rational functions on smooth Jordan curves and arcs. The results are formulated in terms of t…
Extremal decomposition problems for p-harmonic radius
Sergei Kalmykov, Elena Prilepkina
We extend classical results by Lavrent'ev and Kufarev concerning the product of the conformal radii of planar non-overlapping domains. We also extend relatively recent results for…
Bernstein type inequalities for rational functions on analytic curves and arcs
Sergei Kalmykov, Béla Nagy
Borwein and Erdélyi proved a Bernstein type inequality for rational functions on the unit circle and on the real line. Here we establish asymptotically sharp extensions of their in…
Extremal decomposition problems in the Euclidean space
Karina Gulyaeva, Sergei Kalmykov, Elena Prilepkina
Composition principles for reduced moduli are extended to the case of domains in the -dimensional Euclidean space, . As a consequence analogues of extremal decomposition th…
Polynomial and rational inequalities on Jordan arcs and domains
Sergei Kalmykov, Béla Nagy
In this paper we prove an asymptotically sharp Bernstein-type inequality for polynomials on analytic Jordan arcs. Also a general statement on mapping of a domain bounded by finitel…
Asymptotically sharp Markov and Schur inequalities on general sets
Sergei Kalmykov, Bela Nagy, Vilmos Totik
Markov's inequality for algebraic polynomials on goes back to more than a century and it is widely used in approximation theory. Its asymptotically sharp form f…
Log-convexity and log-concavity for series in gamma ratios and applications
S. I. Kalmykov, D. B. Karp
Polynomial sequence is -logarithmically concave if is a polynomial with nonnegative coefficients for any . We introduce an an…
Log-concavity for series in reciprocal gamma functions and applications
S. I. Kalmykov, D. B. Karp
Euler's gamma function is logarithmically convex on positive semi-axis. Additivity of logarithmic convexity implies that the function sum of gammas with non-negative coefficients i…