@Article{Ambrosio2020,
author = "Ambrosio, Vincenzo",
title = "On some convergence results for fractional periodic Sobolev spaces",
journal = "Opuscula Math.",
year = "2020",
volume = "40",
number = "1",
pages = "5--20",
doi = "https://doi.org/10.7494/OpMath.2020.40.1.5",
url = "https://doi.org/10.7494/OpMath.2020.40.1.5",
abstract = "In this note we extend the well-known limiting formulas due to Bourgain-Brezis-Mironescu and Maz'ya-Shaposhnikova, to the setting of fractional Sobolev spaces on the torus. We also give a \(\Gamma\)-convergence result in the spirit of Ponce. The main theorems are obtained by using the nice structure of Fourier series.",
keywords = "fractional periodic Sobolev spaces, Fourier series, \(\Gamma\)-convergence",
issn = "1232-9274"
}