Vengono presentate alcune connessioni tra gli spazi classici delle funzioni a variazione limitata ed altre classi di funzioni la cui variazione è opportunamente controllata, cioè le classi GBV introdotte da E. De Giorgi e L. Ambrosio, e le classi BBV, LBV, GBV* introdotte in questa Nota. Le dimostrazioni dei risultati enunciati, insieme con altri dettagli, appariranno in un successivo lavoro.
We give sufficient conditions for the discreteness of the spectrum of differential operators of the form in where and for Schrödinger operators in . Our conditions are also necessary in the case of polynomial coefficients.
We prove a characterisation of sets with finite perimeter and functions in terms of the short time behaviour of the heat semigroup in . For sets with smooth boundary a more precise result is shown.
In this paper we define jump set and approximate limits for BV functions on Wiener spaces and show that the weak gradient admits a decomposition similar to the finite dimensional case. We also define the SBV class of functions of special bounded variation and give a characterisation of SBV via a chain rule and a closure theorem. We also provide a characterisation of BV functions in terms of the short-time behaviour of the Ornstein-Uhlenbeck semigroup following an approach due to Ledoux.
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