On the approximate form of Kluvánek's theorem

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On the approximate form of Kluvánek's theorem. / Beaty, Michael; Dodson, Maurice; Eveson, Simon; Higgins, John.

In: Journal of Approximation Theory, Vol. 160, No. 1-2, 09.2009, p. 281-303.

Research output: Contribution to journalArticle

Harvard

Beaty, M, Dodson, M, Eveson, S & Higgins, J 2009, 'On the approximate form of Kluvánek's theorem', Journal of Approximation Theory, vol. 160, no. 1-2, pp. 281-303. https://doi.org/10.1016/j.jat.2009.02.013

APA

Beaty, M., Dodson, M., Eveson, S., & Higgins, J. (2009). On the approximate form of Kluvánek's theorem. Journal of Approximation Theory, 160(1-2), 281-303. https://doi.org/10.1016/j.jat.2009.02.013

Vancouver

Beaty M, Dodson M, Eveson S, Higgins J. On the approximate form of Kluvánek's theorem. Journal of Approximation Theory. 2009 Sep;160(1-2):281-303. https://doi.org/10.1016/j.jat.2009.02.013

Author

Beaty, Michael ; Dodson, Maurice ; Eveson, Simon ; Higgins, John. / On the approximate form of Kluvánek's theorem. In: Journal of Approximation Theory. 2009 ; Vol. 160, No. 1-2. pp. 281-303.

Bibtex - Download

@article{362e57ce30334336a2049263dc4ef663,
title = "On the approximate form of Kluv{\'a}nek's theorem",
abstract = "An abstract form of the classical approximate sampling theorem is proved for functions on a locally compact abelian group that are continuous, square-integrable and have integrable Fourier transforms. An additional hypothesis that the samples of the function are square-summable is needed to ensure the convergence of the sampling series. As well as establishing the representation of the function as a sampling series plus a remainder term, an asymptotic formula is obtained under mild additional restrictions on the group. In conclusion a converse to Kluv{\'a}nek's theorem is established.",
keywords = "Analysis, , Pure Mathematics",
author = "Michael Beaty and Maurice Dodson and Simon Eveson and John Higgins",
year = "2009",
month = sep,
doi = "10.1016/j.jat.2009.02.013",
language = "English",
volume = "160",
pages = "281--303",
journal = "Journal of Approximation Theory",
issn = "0021-9045",
publisher = "Academic Press Inc.",
number = "1-2",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - On the approximate form of Kluvánek's theorem

AU - Beaty, Michael

AU - Dodson, Maurice

AU - Eveson, Simon

AU - Higgins, John

PY - 2009/9

Y1 - 2009/9

N2 - An abstract form of the classical approximate sampling theorem is proved for functions on a locally compact abelian group that are continuous, square-integrable and have integrable Fourier transforms. An additional hypothesis that the samples of the function are square-summable is needed to ensure the convergence of the sampling series. As well as establishing the representation of the function as a sampling series plus a remainder term, an asymptotic formula is obtained under mild additional restrictions on the group. In conclusion a converse to Kluvánek's theorem is established.

AB - An abstract form of the classical approximate sampling theorem is proved for functions on a locally compact abelian group that are continuous, square-integrable and have integrable Fourier transforms. An additional hypothesis that the samples of the function are square-summable is needed to ensure the convergence of the sampling series. As well as establishing the representation of the function as a sampling series plus a remainder term, an asymptotic formula is obtained under mild additional restrictions on the group. In conclusion a converse to Kluvánek's theorem is established.

KW - Analysis,

KW - Pure Mathematics

UR - http://www.scopus.com/inward/record.url?scp=70349843886&partnerID=8YFLogxK

U2 - 10.1016/j.jat.2009.02.013

DO - 10.1016/j.jat.2009.02.013

M3 - Article

VL - 160

SP - 281

EP - 303

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

SN - 0021-9045

IS - 1-2

ER -