13 citations · 32 across the 13 of their papers we have counts for
13 papers
On Asymptotic Properties of Certain -Splines in Terms of Theta-like Functions
Michael I. Ganzburg
The asymptotic behavior of the Mellin transform of the associated -splines with special knots in terms of theta-like functions is found. The proof is b…
Discretization Theorems for Entire Functions of Exponential Type
Michael I. Ganzburg
We prove --discretization inequalities for entire functions of exponential type in the form \ba C_2\|f\|_{L_q(\R^m)} \le \left(\sum_{ν=1}^\iy \left\vert f\left(X_ν\r…
Bernstein-Nikolskii Inequality: Optimality with Respect to the Smoothness Parameter
Michael I Ganzburg, Miquel Saucedo, Sergey Tikhonov
In this paper, we study the form of the constant in the Bernstein--Nikolskii inequalities , for trigonom…
A Note on Sharp Multivariate Bernstein- and Markov-Type Inequalities
Michael I. Ganzburg
Let be a symmetric convex body in . We prove sharp Bernstein-type inequalities for entire functions of exponential type with the spectrum in and discuss certain prope…
Asymptotic Relations Between Interpolation Differences and Zeta Functions
Michael I. Ganzburg
Asymptotic relations between zeta functions (such as, , and other Dirichlet -functions) and interpolation differences of functions like and their i…
Asymptotic Behaviour of the Error of Polynomial Approximation of Functions Like
Michael I. Ganzburg
New asymptotic relations between the -errors of best approximation of univariate functions by algebraic polynomials and entire functions of exponential type are obtained for $…
Asymptotics of Sharp Constants in Markov-Bernstein-Nikolskii type Inequalities with Exponential Weights
Michael I. Ganzburg
We prove that the sharp constant in the univariate Bernstein--Nikolskii inequality for entire functions of exponential type is the limit of the sharp constant in the V. A. Markov t…
Sharp Constants of Approximation Theory. VI. Weighted Polynomial Inequalities of Different Metrics on the Multidimensional Cube and Ball
Michael I. Ganzburg
We prove limit equalities between the sharp constants in weighted Nikolskii-type inequalities for multivariate polynomials on an -dimensional cube and ball and the corresponding…
Sharp Constants of Approximation Theory. V. An Asymptotic Equality Related to Polynomials with Given Newton Polyhedra
Michael Ganzburg
Let be a convex body, symmetric about all coordinate hyperplanes, and let $\PP_{aV},\, a\ge 0$, be a set of all algebraic polynomials whose Newton polyhedra are subs…
Sharp Constants of Approximation Theory. IV. Asymptotic Relations in General Settings
Michael I. Ganzburg
In this paper we first introduce the unified definition of the sharp constant that includes constants in three major problems of approximation theory, such as, inequalities for app…
Sharp Constants of Approximation Theory. III. Certain Polynomial Inequalities of Different Metrics on Convex Sets
Michael I. Ganzburg
Let be a centrally symmetric convex body and let be its polar. We prove limit relations between the sharp constants in the multivariate Markov-Berns…
Sharp Constants of Approximation Theory. II. Invariance Theorems and Certain Multivariate Inequalities of Different Metrics
Michael I. Ganzburg
We prove invariance theorems for general inequalities of different metrics and apply them to limit relations between the sharp constants in the multivariate Markov-Bernstein-Nikols…
Sharp Constants of Approximation Theory. I. Multivariate Bernstein-Nikolskii Type Inequalities
Michael I. Ganzburg
We prove limit relations between the sharp constants in the multivariate Bernstein-Nikolskii type inequalities for trigonometric polynomials and entire functions of exponential typ…