On the rate of convergence of a lacunary trigonometric interpolation process

Szabados, J.

doi:10.1007/bf01953973

Cited by 8 publications

(3 citation statements)

References 4 publications

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“…Without loss of generality we may assume that p n ∈ P 1 s n is the best approximation of n out of P 1 s n in C[− 0 , 0 ] norm. Using Lemma 2 from [7] we obtain by (6.9) Here by (7.8)…”

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confidence: 95%

Jackson-type theorems in homogeneous approximation

Kroó

Szabados

2008

Journal of Approximation Theory

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The classical Weierstrass theorem states that any function continuous on a compact set K ⊂ R d (d 1) can be uniformly approximated by algebraic polynomials. In this paper we study the possible extensions of this celebrated result for approximation by homogeneous algebraic polynomials on star-like and convex surfaces in R d such that K = −K. A previous conjecture states that functions continuous on a convex surface can be approximated by a pair of homogeneous polynomials. We verify this conjecture under the mild condition of Dini-Lipschitz smoothness of the convex surface considered. It is also shown that the density fails on surfaces with outer cusps. In addition, we give Jackson-type estimates for the rate of best approximation by homogeneous polynomials on convex surfaces. A new phenomenon here consists of the fact that this rate depends not only on the moduli of continuity of the functions considered, but also on the smoothness properties of convex surfaces.

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“…Without loss of generality we may assume that p n ∈ P 1 s n is the best approximation of n out of P 1 s n in C[− 0 , 0 ] norm. Using Lemma 2 from [7] we obtain by (6.9) Here by (7.8)…”

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confidence: 95%

Jackson-type theorems in homogeneous approximation

Kroó

Szabados

2008

Journal of Approximation Theory

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“…Recently, many works have been devoted to studying the Hermite interpolation and Birkhoff interpolation. Here we only mention a very small part of them, for example, see [1][2][3][4]. As we know, these interpolations are only adequate for smooth functions.…”

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confidence: 99%

On a new kind of 2-periodic trigonometric interpolation

Jiang¹,

Ma²

1996

Appl. Math.

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“…Here we only mention a very small number of them, for example, see [1][2][3][4] . As we know, these interpolations are only adequate to smooth functions .…”

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confidence: 99%