Uniform Approximation of Differentiation Operators by Bounded Linear Operators in the Space Lr

Arestov, V. V.

doi:10.1007/s10476-020-0040-z

Cited by 8 publications

(3 citation statements)

References 22 publications

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“…The following statement is contained in the author's paper [8, Theorem 3]; however, this result was preceded by several years of research by the author, see [4][5][6]8] and [13,14].…”

Section: Two Extremal Problems Related To Stechkin's Problem (12)mentioning

confidence: 99%

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APPROXIMATION OF DIFFERENTIATION OPERATORS BY BOUNDED LINEAR OPERATORS IN LEBESGUE SPACES ON THE AXIS AND RELATED PROBLEMS IN THE SPACES OF $(p,q)$-MULTIPLIERS AND THEIR PREDUAL SPACES

Arestov

2023

UMJ

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We consider a variant $E_{n,k}(N;r,r;p,p)$ of the four-parameter Stechkin problem $E_{n,k}(N;r,s;p,q)$ on the best approximation of differentiation operators of order $k$ on the class of $n$ times differentiable functions $(0<k<n)$ in Lebesgue spaces on the real axis. We discuss the state of research in this problem and related problems in the spaces of multipliers of Lebesgue spaces and their predual spaces. We give two-sided estimates for $E_{n,k}(N;r,r;p,p)$. The paper is based on the author's talk at the S.B. Stechkin's International Workshop-Conference on Function Theory (Kyshtym, Chelyabinsk region, August 1–10, 2023).

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“…The following statement is contained in the author's paper [8, Theorem 3]; however, this result was preceded by several years of research by the author, see [4][5][6]8] and [13,14].…”

Section: Two Extremal Problems Related To Stechkin's Problem (12)mentioning

confidence: 99%

“…The following inequality holds [11,13] for the best constants in (3.39) and, in particular, in (3.40):…”

Section: Case N = 2 R =mentioning

confidence: 99%

APPROXIMATION OF DIFFERENTIATION OPERATORS BY BOUNDED LINEAR OPERATORS IN LEBESGUE SPACES ON THE AXIS AND RELATED PROBLEMS IN THE SPACES OF $(p,q)$-MULTIPLIERS AND THEIR PREDUAL SPACES

Arestov

2023

UMJ

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“…For a good overview of known results on the Stechkin problem and discussion of related questions we refer the reader to surveys [1,3], book [6] and recent paper [2].…”

Section: Introductionmentioning

confidence: 99%

The best approximation of closed operators by bounded operators in Hilbert spaces

Бабенко

Parfinovych

Skorokhodov

2022

Carpathian Math. Publ.

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We solve the problem of the best approximation of closed operators by linear bounded operators in Hilbert spaces under assumption that the operator transforms orthogonal basis in Hilbert space into an orthogonal system. As a consequence, sharp additive Hardy-Littlewood-Pólya type inequality for multiple closed operators is established. We also demonstrate application of these results in concrete situations: for the best approximation of powers of the Laplace-Beltrami operator on classes of functions defined on closed Riemannian manifolds, for the best approximation of differentiation operators on classes of functions defined on the period and on the real line with the weight $e^{-x^2}$, and for the best approximation of functions of self-adjoint operators in Hilbert spaces.

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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

Arestov

2022

Anal Math

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Uniform Approximation of Differentiation Operators by Bounded Linear Operators in the Space Lr

Cited by 8 publications

References 22 publications

APPROXIMATION OF DIFFERENTIATION OPERATORS BY BOUNDED LINEAR OPERATORS IN LEBESGUE SPACES ON THE AXIS AND RELATED PROBLEMS IN THE SPACES OF \((p,q)\)-MULTIPLIERS AND THEIR PREDUAL SPACES

APPROXIMATION OF DIFFERENTIATION OPERATORS BY BOUNDED LINEAR OPERATORS IN LEBESGUE SPACES ON THE AXIS AND RELATED PROBLEMS IN THE SPACES OF \((p,q)\)-MULTIPLIERS AND THEIR PREDUAL SPACES

The best approximation of closed operators by bounded operators in Hilbert spaces

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

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