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- ItemLocal approximation of arbitrary functions by solutions of nonlocal equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Dipierro, Serena; Savin, Ovidiu; Valdinoci, EnricoWe show that any function can be locally approximated by solutions of prescribed linear equations of nonlocal type. In particular, we show that every function is locally s-caloric, up to a small error. The case of non-elliptic and non-parabolic operators is taken into account as well.
- ItemAll functions are locally s-harmonic up to a small error(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Dipierro, Serena; Savin, Ovidiu; Valdinoci, EnricoWe show that we can approximate every function f Ck (B1) with a s-harmonic function in B1 that vanishes outside a compact set. That is, s-harmonic functions are dense in Ck loc. This result is clearly in contrast with the rigidity of harmonic functions in the classical case and can be viewed as a purely nonlocal feature.