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∏‐Variation with Remainder
Author(s) -
Omey E.,
Willekens E.
Publication year - 1988
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-37.121.105
Subject(s) - remainder , class (philosophy) , variation (astronomy) , mathematics , function (biology) , combinatorics , pure mathematics , arithmetic , physics , computer science , artificial intelligence , astrophysics , evolutionary biology , biology
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 → ∞ for t > 0. We also discuss Abel‐Tauber‐Mercer theorems for a class of integral transforms of these functions.