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 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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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. 
@article{RLIN_2000_9_11_1_a1,
     author = {Metafune, Giorgio and Pallara, Diego},
     title = {Discreteness of the spectrum for some differential operators with unbounded coefficients in \( {\mathbb{R}^{n}} \)},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {9--19},
     year = {2000},
     volume = {Ser. 9, 11},
     number = {1},
     zbl = {0982.35078},
     mrnumber = {MR1797049},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2000_9_11_1_a1/}
}
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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/