Dopo aver ricordato alcune delle proprietà delle basi di wavelets, ed in particolare la proprietà di caratterizzazione di spazi funzionali tramite coefficienti wavelet, descriviamo due nuovi approcci rispettivamente alla stabilizzazione di problemi numericamente instabili ed alla soluzione nonlineare (adattativa) di equazioni differenziali alle derivate parziali, che sono resi possibili da dette proprietà.
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