Sharp Bernstein Type Inequalities for Splines in the Mean Square Metrics

Standard

Sharp Bernstein Type Inequalities for Splines in the Mean Square Metrics. / Vinogradov, O. L.

In: Journal of Mathematical Sciences (United States), Vol. 215, No. 5, 2016, p. 595-600.

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

Author

Vinogradov, O. L. / Sharp Bernstein Type Inequalities for Splines in the Mean Square Metrics. In: Journal of Mathematical Sciences (United States). 2016 ; Vol. 215, No. 5. pp. 595-600.

BibTeX

@article{a9dfabaf907f47b8accb7500330cc560,

title = "Sharp Bernstein Type Inequalities for Splines in the Mean Square Metrics",

abstract = "We give an elementary proof of the sharp Bernstein type inequality(Formula presented.). Here n, r, s ∈ ℕ, f is a 2π-periodic spline of order r and of minimal defect with nodes jπ/n, j ∈ Z, δh sis the difference operator of order s with step h, and the Kmare the Favard constants. A similar inequality for the space L2(ℝ) is also established. Bibliography: 5 titles.",

keywords = "Discrete Fourier Transform, Spline Space, Basic Spline, Sharp Inequality, Bernstein Inequality",

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

note = "Vinogradov, O.L. Sharp Bernstein Type Inequalities for Splines in the Mean Square Metrics. J Math Sci 215, 595–600 (2016). https://doi.org/10.1007/s10958-016-2865-3",

year = "2016",

doi = "10.1007/s10958-016-2865-3",

language = "English",

volume = "215",

pages = "595--600",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "5",

}

RIS

TY - JOUR

T1 - Sharp Bernstein Type Inequalities for Splines in the Mean Square Metrics

AU - Vinogradov, O. L.

N1 - Vinogradov, O.L. Sharp Bernstein Type Inequalities for Splines in the Mean Square Metrics. J Math Sci 215, 595–600 (2016). https://doi.org/10.1007/s10958-016-2865-3

PY - 2016

Y1 - 2016

N2 - We give an elementary proof of the sharp Bernstein type inequality(Formula presented.). Here n, r, s ∈ ℕ, f is a 2π-periodic spline of order r and of minimal defect with nodes jπ/n, j ∈ Z, δh sis the difference operator of order s with step h, and the Kmare the Favard constants. A similar inequality for the space L2(ℝ) is also established. Bibliography: 5 titles.

AB - We give an elementary proof of the sharp Bernstein type inequality(Formula presented.). Here n, r, s ∈ ℕ, f is a 2π-periodic spline of order r and of minimal defect with nodes jπ/n, j ∈ Z, δh sis the difference operator of order s with step h, and the Kmare the Favard constants. A similar inequality for the space L2(ℝ) is also established. Bibliography: 5 titles.

KW - Discrete Fourier Transform

KW - Spline Space

KW - Basic Spline

KW - Sharp Inequality

KW - Bernstein Inequality

UR - http://www.scopus.com/inward/record.url?scp=84965066773&partnerID=8YFLogxK

U2 - 10.1007/s10958-016-2865-3

DO - 10.1007/s10958-016-2865-3

M3 - Article

AN - SCOPUS:84965066773

VL - 215

SP - 595

EP - 600

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 15680280