Construction of Continuous, Integrable Functions with Extreme Behavior at Infinity

2010/10/16 by George W. Batten, George W. Batten Jr, Batten, George W.
Mathematics · #26A06 #26A12 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #advanced mathematical theories #math.CA #msc:26A06 #msc:26A12

paper · pdf · doi:10.48550/arxiv.1010.3354

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

openalex publication_date 2010/10/16 · arxiv created 2011/01/20 · arxiv updated 2011/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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