Results 21 to 27 of about 33 (27)

Stechkin's problem for functions of a self-adjoint operator in a Hilbert space, Taikov-type inequalities and their applications

, 2017
In this paper we solve the problem of approximating functionals $(φ(A)x, f)$ (where $φ(A)$ is some function of self-adjoint operator $A$) on the class of elements of a Hilbert space that is defined with the help of another function $ψ(A)$ of the operator $A$.
Babenko, Vladyslav, Babenko, Yuliya, Kriachko, Nadiia   +2 more
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Stechkin’s Problem on the Best Approximation of an Unbounded Operator by Bounded Ones and Related Problems

, 2022
This paper discusses Stechkin’s problem on the best approximation of a linear unbounded operator by bounded linear operators and related extremal problems. The main attention is paid to the approximation of differentiation operators in Lebesgue spaces on the axis and to the operator of the continuation of an analytic function to a domain from a part of
Arestov, V. V., Akopyan, R. R.
openaire   +1 more source

A decoupling interpretation of an old argument for Vinogradov's Mean Value Theorem

Mathematika, Volume 70, Issue 1, January 2024.
Abstract We interpret into decoupling language a refinement of a 1973 argument due to Karatsuba on Vinogradov's mean value theorem. The main goal of our argument is to answer what precisely solution counting in older partial progress on Vinogradov's mean value theorem corresponds to in Fourier decoupling theory.
Brian Cook, Kevin Hughes, Zane Kun Li, Akshat Mudgal, Olivier Robert, Po‐Lam Yung   +5 more
wiley   +1 more source

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Predual Spaces for the Space of (p, q)-Multipliers and Their Application in Stechkin’s Problem on Approximation of Differentiation Operators

Analysis Mathematica, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Stechkin’s Problem on Approximation of the Differentiation Operator in the Uniform Norm on the Half-Line

Mathematical Notes
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Akopyan, R. R., Arestov, V. V., Timofeev, V. G.   +2 more
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The stechkin problem for partial derivation operators on classes of finitely smooth functions

Mathematical Notes, 2000
Let \(D\) be a domain of \(\mathbb{R}^d\), \(h\in\mathbb{R}^d\), \(D_h= \{x\in D: x+th\in D\) for all \(t\in [0,1]\}\), \(\Delta_hf(x)= f(x+ h)- f(x)\) for \(x\in D_h\) and \(f: D\to\mathbb{R}\), \(\Delta^0_hf=f\), \(\Delta^m_hf(x)= \Delta_h(\Delta^{m-1}_h f)(x)\) for \(m\in\mathbb{Z}_+\) and \(x\in D_{mh}\), \(\Omega^m(f, t)_p= \text{ess sup}\{|\Delta^
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A Variant of Stechkin’s Problem on the Best Approximation of a Fractional Order Differentiation Operator on the Axis

Proceedings of the Steklov Institute of Mathematics
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