Analogs of the Riesz Identity, and Sharp Inequalities for Derivatives and Differences of Splines in the Integral Metric

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Analogs of the Riesz Identity, and Sharp Inequalities for Derivatives and Differences of Splines in the Integral Metric. / Vinogradov, O. L.

в: Journal of Mathematical Sciences (United States), Том 251, № 2, 22.10.2020, стр. 215-226.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{9edadf9989894500bb8e24cbee21cf07,

title = "Analogs of the Riesz Identity, and Sharp Inequalities for Derivatives and Differences of Splines in the Integral Metric",

abstract = "An analog of the Riesz interpolation formula is established. It allows us to obtain a sharp estimate for the first order derivative of a spline of minimal defect with equidistant knots jπσ,j∈ℤ, in terms of the first order difference in the integral metric. Moreover, the constructed identity makes it possible to strengthen the inequality by replacing its right-hand side with a linear combination of differences, including higher order differences, of the spline. In the case of the difference step πσ, iterations of this identity lead to formulas analogous to the Riesz formula for higher order derivatives and differences; this allows us to obtain Riesz and Bernstein type inequalities for them, also in a stronger form.",

author = "Vinogradov, {O. L.}",

note = "Vinogradov, O.L. Analogs of the Riesz Identity, and Sharp Inequalities for Derivatives and Differences of Splines in the Integral Metric. J Math Sci 251, 215–226 (2020). https://doi.org/10.1007/s10958-020-05082-8",

year = "2020",

month = oct,

day = "22",

doi = "10.1007/s10958-020-05082-8",

language = "English",

volume = "251",

pages = "215--226",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "2",

}

RIS

TY - JOUR

T1 - Analogs of the Riesz Identity, and Sharp Inequalities for Derivatives and Differences of Splines in the Integral Metric

AU - Vinogradov, O. L.

N1 - Vinogradov, O.L. Analogs of the Riesz Identity, and Sharp Inequalities for Derivatives and Differences of Splines in the Integral Metric. J Math Sci 251, 215–226 (2020). https://doi.org/10.1007/s10958-020-05082-8

PY - 2020/10/22

Y1 - 2020/10/22

N2 - An analog of the Riesz interpolation formula is established. It allows us to obtain a sharp estimate for the first order derivative of a spline of minimal defect with equidistant knots jπσ,j∈ℤ, in terms of the first order difference in the integral metric. Moreover, the constructed identity makes it possible to strengthen the inequality by replacing its right-hand side with a linear combination of differences, including higher order differences, of the spline. In the case of the difference step πσ, iterations of this identity lead to formulas analogous to the Riesz formula for higher order derivatives and differences; this allows us to obtain Riesz and Bernstein type inequalities for them, also in a stronger form.

AB - An analog of the Riesz interpolation formula is established. It allows us to obtain a sharp estimate for the first order derivative of a spline of minimal defect with equidistant knots jπσ,j∈ℤ, in terms of the first order difference in the integral metric. Moreover, the constructed identity makes it possible to strengthen the inequality by replacing its right-hand side with a linear combination of differences, including higher order differences, of the spline. In the case of the difference step πσ, iterations of this identity lead to formulas analogous to the Riesz formula for higher order derivatives and differences; this allows us to obtain Riesz and Bernstein type inequalities for them, also in a stronger form.

UR - http://www.scopus.com/inward/record.url?scp=85093838213&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/f57a6e7b-b956-3985-bd23-a3f531cd8aa5/

U2 - 10.1007/s10958-020-05082-8

DO - 10.1007/s10958-020-05082-8

M3 - Article

AN - SCOPUS:85093838213

VL - 251

SP - 215

EP - 226

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 2

ER -

ID: 72082127