Estimates of the norm of a function orthogonal to the piecewise-constant functions in terms of higher-order moduli of continuity

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Estimates of the norm of a function orthogonal to the piecewise-constant functions in terms of higher-order moduli of continuity. / Vinogradov, O. L.; Ikhsanov, L. N.

In: Vestnik St. Petersburg University: Mathematics, Vol. 49, No. 1, 01.01.2016, p. 5-8.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{c55f664c19e14e64acd12f8aaf802b0b,

title = "Estimates of the norm of a function orthogonal to the piecewise-constant functions in terms of higher-order moduli of continuity",

abstract = "The uniform norm of a function that is defined on the real line and has zero integrals between integer points is estimated in terms of its modulus of continuity of arbitrary even order. Sharp bounds of this kind are known for periodic functions. The passage to nonperiodic functions significantly complicates the problem. In general, the constant for nonperiodic functions is greater than that for periodic functions. The constants in the bound are improved compared with those known earlier. The proof is based on a representation of the error of the polynomial interpolation as the product of the influence polynomial and an integrated difference of higher order.",

keywords = "mean interpolation, modulus of continuity",

author = "Vinogradov, {O. L.} and Ikhsanov, {L. N.}",

year = "2016",

month = jan,

day = "1",

doi = "10.3103/S106345411601012X",

language = "English",

volume = "49",

pages = "5--8",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - Estimates of the norm of a function orthogonal to the piecewise-constant functions in terms of higher-order moduli of continuity

AU - Vinogradov, O. L.

AU - Ikhsanov, L. N.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - The uniform norm of a function that is defined on the real line and has zero integrals between integer points is estimated in terms of its modulus of continuity of arbitrary even order. Sharp bounds of this kind are known for periodic functions. The passage to nonperiodic functions significantly complicates the problem. In general, the constant for nonperiodic functions is greater than that for periodic functions. The constants in the bound are improved compared with those known earlier. The proof is based on a representation of the error of the polynomial interpolation as the product of the influence polynomial and an integrated difference of higher order.

AB - The uniform norm of a function that is defined on the real line and has zero integrals between integer points is estimated in terms of its modulus of continuity of arbitrary even order. Sharp bounds of this kind are known for periodic functions. The passage to nonperiodic functions significantly complicates the problem. In general, the constant for nonperiodic functions is greater than that for periodic functions. The constants in the bound are improved compared with those known earlier. The proof is based on a representation of the error of the polynomial interpolation as the product of the influence polynomial and an integrated difference of higher order.

KW - mean interpolation

KW - modulus of continuity

UR - http://www.scopus.com/inward/record.url?scp=84979622713&partnerID=8YFLogxK

U2 - 10.3103/S106345411601012X

DO - 10.3103/S106345411601012X

M3 - Article

AN - SCOPUS:84979622713

VL - 49

SP - 5

EP - 8

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -

ID: 15680224