5 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…
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…