$\pi$-Variation with remainder

E. Omey; E.K.E. Willekens

doi:10.1112/jlms/s2-37.121.105

$\pi$-Variation with remainder

E. Omey, E.K.E. Willekens

Mathematics and Computer Science

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

10 Citations (Scopus)

Abstract

Let b: R+ ¿ R+ be an O-regularly varying function. In this paper we are concerned with the class of functions L for which there exists a function a: R+ ¿ R such that L(tx) - L(x) - a(x) log(t) = O(b(x)) as x ¿ 8 for t > 0. We also discuss Abel-Tauber-Mercer theorems for a class of integral transforms of these functions.

Original language	English
Pages (from-to)	105-118
Journal	Journal of the London Mathematical Society. Second Series
Volume	37
DOIs	https://doi.org/10.1112/jlms/s2-37.121.105
Publication status	Published - 1988

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10.1112/jlms/s2-37.121.105

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title = "$\pi$-Variation with remainder",

abstract = "Let b: R+ ¿ R+ be an O-regularly varying function. In this paper we are concerned with the class of functions L for which there exists a function a: R+ ¿ R such that L(tx) - L(x) - a(x) log(t) = O(b(x)) as x ¿ 8 for t > 0. We also discuss Abel-Tauber-Mercer theorems for a class of integral transforms of these functions.",

author = "E. Omey and E.K.E. Willekens",

year = "1988",

doi = "10.1112/jlms/s2-37.121.105",

language = "English",

volume = "37",

pages = "105--118",

journal = "Journal of the London Mathematical Society. Second Series",

issn = "0024-6107",

publisher = "Oxford University Press",

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TY - JOUR

T1 - $\pi$-Variation with remainder

AU - Omey, E.

AU - Willekens, E.K.E.

PY - 1988

Y1 - 1988

N2 - Let b: R+ ¿ R+ be an O-regularly varying function. In this paper we are concerned with the class of functions L for which there exists a function a: R+ ¿ R such that L(tx) - L(x) - a(x) log(t) = O(b(x)) as x ¿ 8 for t > 0. We also discuss Abel-Tauber-Mercer theorems for a class of integral transforms of these functions.

AB - Let b: R+ ¿ R+ be an O-regularly varying function. In this paper we are concerned with the class of functions L for which there exists a function a: R+ ¿ R such that L(tx) - L(x) - a(x) log(t) = O(b(x)) as x ¿ 8 for t > 0. We also discuss Abel-Tauber-Mercer theorems for a class of integral transforms of these functions.

U2 - 10.1112/jlms/s2-37.121.105

DO - 10.1112/jlms/s2-37.121.105

M3 - Article

SN - 0024-6107

VL - 37

SP - 105

EP - 118

JO - Journal of the London Mathematical Society. Second Series

JF - Journal of the London Mathematical Society. Second Series

ER -

$\pi$-Variation with remainder

Abstract

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