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

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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. 
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     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},
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     publisher = {mathdoc},
     volume = {Ser. 9, 11},
     number = {1},
     year = {2000},
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     mrnumber = {MR1797049},
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     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/