On some convergence results for fractional periodic Sobolev spaces

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