arXiv:1010.3354 Abstract | arXiv Analytics

arXiv:1010.3354 [math.CA]Abstract References Reviews Resources

Construction of Continuous, Integrable Functions with Extreme Behavior at Infinity

Published 2010-10-16, updated 2011-01-20Version 4

For any real sequence {c(n)} tending to infinity as n tends to infinity, this constructs a function f which is continuous and integrable, and such that for every nonzero x, limsup c(n) f(n x) is infinite.

Comments: 8 pages, LaTeX. Corrected 2010Dec15. Minor corrections made 2011Jan18, especially E contains instead of E equals in the 6th line above section 2; some comments added

Categories: math.CA

Subjects: 26A12, 26A06

Keywords: extreme behavior, integrable functions, construction, continuous

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