Geodesic
Discreteness of the spectrum for some differential operators with unbounded coefficients in \( \mathbb{R}^{n} \)
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 11 (2000) no. 1, pp. 9-19.

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We give sufficient conditions for the discreteness of the spectrum of differential operators of the form \( A u = - \triangle u + ( \nabla F,\nabla u) \) in \( L^{2}_{\mu}(\mathbb{R}^{n}) \) where \( d \mu(x) = e^{-F(x)} dx \) and for Schrödinger operators in \( L^{2}(\mathbb{R}^{n}) \). Our conditions are also necessary in the case of polynomial coefficients.
In questa Nota si studiano operatori della forma \( A u = - \triangle u + ( \nabla F,\nabla u) \) in \( L^{2}_{\mu}(\mathbb{R}^{n}) \) con \( d \mu(x) = e^{-F(x)} dx \), e operatori di Schrödinger in \( L^{2}(\mathbb{R}^{n}) \). Si danno condizioni sufficienti affinché lo spettro di un tale operatore differenziale sia discreto. Le condizioni trovate sono anche necessarie nel caso di coefficienti polinomiali. 
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Metafune, Giorgio; Pallara, Diego. Discreteness of the spectrum for some differential operators with unbounded coefficients in \( \mathbb{R}^{n} \). Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 11 (2000) no. 1, pp. 9-19. http://geodesic.mathdoc.fr/item/RLIN_2000_9_11_1_a1/

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