arXiv subjects

Vladislav Babenko

Publications and source records attributed to Vladislav Babenko.

6 recordsLinked to original sources

arXiv2020

On the Hardy-Littlewood-P\'olya and Taikov type inequalities for multiple operators in Hilbert spaces

We present unified approach to obtain sharp mean-squared and multiplicative inequalities of Hardy-Littlewood-Poly\'a and Taikov types for multiple closed operators acting on Hilbert space. We apply our results to establish new sharp inequalities for the norms of powers of the Laplace-Beltrami operators on compact Riemmanian manifolds and derive the well-known Taikov and Hardy-Littlewood-Poly\'a inequalities for functions defined on $d$-dimensional space in the limit case. Other applications include the best approximation of unbounded operators by linear bounded ones and the best approximation of one class by elements of other class. In addition, we establish sharp Solyar-type inequalities for unbounded closed operators with closed range.

math.FA↗

arXiv2017

Estimation of wavelet coefficients on some classes of functions

Let $Ψ_m^D$ be orthogonal Daubechies wavelets that have m zero moments and let $$ W_{2,p}^k=\{f \in L_2(R):\|(I ω)^k\hat f(ω)\|_p\leq 1\}, \, k \in N. $$ We prove that $$ \lim_{m \to \infty}\, \sup\left\{\frac{|(Ψ_m^D)|}{\|(\hat Ψ_m^D)\|_q}: f \in W_{2, p'}^k\right\}=\frac{\frac{(2π)^{1/p-1/2}}{π^k}\left(\frac{1-2^{1-pk}}{pk-1}\right)^{1/p}}{(2π)^{1/q-1/2}}. $$

math.FA↗

arXiv2017

Inequalities similar to those of Bernstein for non-periodic splines in $L_2$ space

We prove Inequalities similar to those of Bernstein for non-periodic splines in $L_2$ space.

math.FA↗

arXiv2014

Sharp Estimates for Norms of Functions from Conjugate Classes in Metrics C and L

Sharp estimates for C - and L - norms of functions that are conjugate with functions from the classes W^rH_ωof periodic functions having prescribed concave majorant of moduli of continuity, as well as sharp estimates for the differences of such functions are obtained.

math.FA↗

arXiv2011

Exact asymptotics of the optimal $L_{p,\Omega}$-error of linear spline interpolation

In this paper we provide the exact asymptotics of the optimal weighted $L_p$-error, $0<p< \infty$, of linear spline interpolation of $C^2$ functions with positive Hessian. The full description of the behavior of the optimal error leads to the algorithm for construction of an asymptotically optimal sequence of triangulations. In addition, we compute the minimum of the $L_p$-error of linear interpolation of the function $x^2+y^2$ over all triangles of unit area for all $0<p<\infty$. This provides the exact constant in the asymptotics of the optimal error.

math.NA↗

arXiv2011

On one extremal property of a regular simplex

In this paper, we show that the $L_p$-error of asymmetric linear approximation of the quadratic function $Q({\mathbf x})=\sum_{j=1}^{d}x_j^2$ on simplices in $\RR^d$ of fixed volume is minimized on regular simplices.

math.NA↗