Variations and Extensions of Croft's Problem
Abstract
We present variations and extensions of the following classical calculus result: If \(f\colon (0,\infty)\to\mathbb R\) is a continuous function, such that, for every positive \(x\), the sequence \(\{f(nx)\}\) tends to zero as \(n\) tends to infinity, then \(f(x)\) also tends to zero, as \(x\) tends to infinity. One of our tools will be Baire's Theorem.
Fields of Study & Subjects
Approximation Theory and Sequence Spaces
Mathematical and Theoretical Analysis
Advanced Harmonic Analysis Research
Publication details
- Journal / source
- Real Analysis Exchange
- Volume
- 51
- Issue
- 1
- Pages
- 205–218
- Publication date
- 10 March 2026
- Language
- EN