On some convergence results for fractional periodic Sobolev spaces
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wersja wydawnicza
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pp. 5-20
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Bibliogr. 19-20.
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.