TY  - JOUR
ID  - Ambrosio2020
LB  - Ambrosio2020
AU  - Ambrosio, Vincenzo
TI  - On some convergence results for fractional periodic Sobolev spaces
ST  - On some convergence results for fractional periodic Sobolev spaces
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2020
VL  - 40
IS  - 1
SP  - 5
EP  - 20
DO  - https://doi.org/10.7494/OpMath.2020.40.1.5
UR  - https://doi.org/10.7494/OpMath.2020.40.1.5
AB  - 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.
KW  - fractional periodic Sobolev spaces
KW  - Fourier series
KW  - \(\Gamma\)-convergence
SN  - 1232-9274
ER  -