Approximation by families of generalized sampling series, realizations of generalized<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi mathvariant="script">K</mml:mi></mml:math>-functionals and generalized moduli of smoothness

Artamonov, S. Yu.; Runovski, K.; Schmeißer, Hans-Jürgen

doi:10.1016/j.jmaa.2020.124138

Cited by 6 publications

(2 citation statements)

References 13 publications

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“…K-functionals and their realizations as well as some special moduli of smoothness) instead of the classical moduli of smoothness (see, e.g., [36,Ch. 9], [1], [24]). For our purposes, it is convenient to use realizations of K-functionals.…”

Section: The Case Of Weak Compatibility Of ϕ and ϕmentioning

confidence: 99%

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Approximation by periodic multivariate quasi-projection operators

Kolomoitsev

Krivoshein

Skopina

2020

Journal of Mathematical Analysis and Applications

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Approximation properties of quasi-projection operators Qj(f, ϕ, ϕ) are studied. Such an operator is associated with a function ϕ satisfying the Strang-Fix conditions and a tempered distribution ϕ such that compatibility conditions with ϕ hold. Error estimates in the uniform norm are obtained for a wide class of quasi-projection operators defined on the space of uniformly continuous functions and on the anisotropic Besov spaces. Under additional assumptions on ϕ and ϕ, two-sided estimates in terms of realizations of the K-functional are also obtained.

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Section: The Case Of Weak Compatibility Of ϕ and ϕmentioning

confidence: 99%

“…In many cases, the realization R ρ (f, M −j ) is equivalent to the corresponding modulus of smoothness or K-functional (see, e.g., [1], [23], [24]). Let us mention some results in this direction.…”

Section: The Case Of Weak Compatibility Of ϕ and ϕmentioning

confidence: 99%

Approximation by periodic multivariate quasi-projection operators

Kolomoitsev

Krivoshein

Skopina

2020

Journal of Mathematical Analysis and Applications

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Uniform approximation by multivariate quasi-projection operators

Kolomoitsev

Skopina

2022

Anal.Math.Phys.

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Approximation properties of quasi-projection operators $$Q_j(f,\varphi , \widetilde{\varphi })$$ Q j ( f , φ , φ ~ ) are studied. These operators are associated with a function $$\varphi $$ φ satisfying the Strang–Fix conditions and a tempered distribution $$\widetilde{\varphi }$$ φ ~ such that compatibility conditions with $$\varphi $$ φ hold. Error estimates in the uniform norm are obtained for a wide class of quasi-projection operators defined on the space of uniformly continuous functions and on the anisotropic Besov-type spaces. Under additional assumptions on $$\varphi $$ φ and $$\widetilde{\varphi }$$ φ ~ , two-sided estimates in terms of realizations of the K-functional are also established.

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A strong converse inequality for generalized sampling operators

Acar

Draganov

2022

Ann. Funct. Anal.

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Approximation by families of generalized sampling series, realizations of generalizedK-functionals and generalized moduli of smoothness

Cited by 6 publications

References 13 publications

Approximation by periodic multivariate quasi-projection operators

Approximation by periodic multivariate quasi-projection operators

Uniform approximation by multivariate quasi-projection operators

A strong converse inequality for generalized sampling operators

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