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Estimates for functionals by deviations of the Riesz sums in seminormed spaces. / Dodonov, N. Yu; Zhuk, V. V.

In: Journal of Mathematical Sciences, Vol. 159, No. 1, 01.05.2009, p. 54-66.

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

Harvard

Dodonov, NY & Zhuk, VV 2009, 'Estimates for functionals by deviations of the Riesz sums in seminormed spaces', Journal of Mathematical Sciences, vol. 159, no. 1, pp. 54-66. https://doi.org/10.1007/s10958-009-9426-y

APA

Dodonov, N. Y., & Zhuk, V. V. (2009). Estimates for functionals by deviations of the Riesz sums in seminormed spaces. Journal of Mathematical Sciences, 159(1), 54-66. https://doi.org/10.1007/s10958-009-9426-y

Vancouver

Dodonov NY, Zhuk VV. Estimates for functionals by deviations of the Riesz sums in seminormed spaces. Journal of Mathematical Sciences. 2009 May 1;159(1):54-66. https://doi.org/10.1007/s10958-009-9426-y

Author

Dodonov, N. Yu ; Zhuk, V. V. / Estimates for functionals by deviations of the Riesz sums in seminormed spaces. In: Journal of Mathematical Sciences. 2009 ; Vol. 159, No. 1. pp. 54-66.

BibTeX

@article{059417c58f7f49189ef7e036c7c85b09,
title = "Estimates for functionals by deviations of the Riesz sums in seminormed spaces",
abstract = "Suppose that (X, p) is a sermonized space, {xk}nk=0 is a linearly independent system of elements in X, {c k}nk=0 is a sequence of linear bounded functionals such that c k (xl) = δkl, Rn,r (x) = n ∑ k=0 (1 - (k/n+1)r) c k(x)xk are the Riesz sums. We prove general assertions concerning estimates from above for the values of semiadditive functionals Φ : X → ℝ+ by deviations of the Riesz sums p(x - R n,r (x)). Bibliography: 6 titles.",
author = "Dodonov, {N. Yu} and Zhuk, {V. V.}",
year = "2009",
month = may,
day = "1",
doi = "10.1007/s10958-009-9426-y",
language = "English",
volume = "159",
pages = "54--66",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "1",

}

RIS

TY - JOUR

T1 - Estimates for functionals by deviations of the Riesz sums in seminormed spaces

AU - Dodonov, N. Yu

AU - Zhuk, V. V.

PY - 2009/5/1

Y1 - 2009/5/1

N2 - Suppose that (X, p) is a sermonized space, {xk}nk=0 is a linearly independent system of elements in X, {c k}nk=0 is a sequence of linear bounded functionals such that c k (xl) = δkl, Rn,r (x) = n ∑ k=0 (1 - (k/n+1)r) c k(x)xk are the Riesz sums. We prove general assertions concerning estimates from above for the values of semiadditive functionals Φ : X → ℝ+ by deviations of the Riesz sums p(x - R n,r (x)). Bibliography: 6 titles.

AB - Suppose that (X, p) is a sermonized space, {xk}nk=0 is a linearly independent system of elements in X, {c k}nk=0 is a sequence of linear bounded functionals such that c k (xl) = δkl, Rn,r (x) = n ∑ k=0 (1 - (k/n+1)r) c k(x)xk are the Riesz sums. We prove general assertions concerning estimates from above for the values of semiadditive functionals Φ : X → ℝ+ by deviations of the Riesz sums p(x - R n,r (x)). Bibliography: 6 titles.

UR - http://www.scopus.com/inward/record.url?scp=67649479386&partnerID=8YFLogxK

U2 - 10.1007/s10958-009-9426-y

DO - 10.1007/s10958-009-9426-y

M3 - Article

AN - SCOPUS:67649479386

VL - 159

SP - 54

EP - 66

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 1

ER -

ID: 35266384