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Uniform oscillation properties of almost periodic functions
Abstract
A synthetic view is provided on scattered results which were never presented in this form in the literature. First we investigate precisely the oscillation length for periodic functions. Then, we establish the existence of a uniform oscillation lentgh for any scalar almost periodic function with mean-value 0. After that, we investigate upper bounds of the oscillation length for some almost periodic functions which appear in the study of continuum mechanics, and we show the existence of a finite oscillation length with respect to time in any open subset of some vibrating continuous media. The paper finally recalls a long standing open problem on the vibrations of a square membrane with fixed edge.
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BibTeX
@misc{haraux2026uniform,
title = {{Uniform oscillation properties of almost periodic functions}},
author = {Alain Haraux},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06515},
eprint = {2610.06515},
archivePrefix = {arXiv},
url = {https://cnrs.hal.science/hal-05777142v1},
}
RIS
TY - UNPB
TI - Uniform oscillation properties of almost periodic functions
AU - Alain Haraux
PY - 2026
DA - 2026/10/04
PB - HAL
DO - 10.48550/arxiv.2610.06515
UR - https://cnrs.hal.science/hal-05777142v1
AB - A synthetic view is provided on scattered results which were never presented in this form in the literature. First we investigate precisely the oscillation length for periodic functions. Then, we establish the existence of a uniform oscillation lentgh for any scalar almost periodic function with mean-value 0. After that, we investigate upper bounds of the oscillation length for some almost periodic functions which appear in the study of continuum mechanics, and we show the existence of a finite oscillation length with respect to time in any open subset of some vibrating continuous media. The paper finally recalls a long standing open problem on the vibrations of a square membrane with fixed edge.
ER -