Construction of Continuous, Integrable Functions with Extreme Behavior at Infinity
Classical Analysis and ODEs
2011-01-21 v4
Abstract
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.
Keywords
Cite
@article{arxiv.1010.3354,
title = {Construction of Continuous, Integrable Functions with Extreme Behavior at Infinity},
author = {George W. Batten},
journal= {arXiv preprint arXiv:1010.3354},
year = {2011}
}
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