Discreteness of the spectrum for some differential operators with unbounded coefficients in $ \mathbb{R}^{n} $

Metafune, Giorgio; Pallara, Diego

Discreteness of the spectrum for some differential operators with unbounded coefficients in

R^{n}

Metafune, Giorgio ; Pallara, Diego

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 11 (2000), p. 9-19 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

We give sufficient conditions for the discreteness of the spectrum of differential operators of the form $A u = - △ u + (\nabla F, \nabla u)$ in $L_{μ}^{2} (R^{n})$ where $d μ (x) = e^{- F (x)} d x$ and for Schrödinger operators in $L^{2} (R^{n})$ . Our conditions are also necessary in the case of polynomial coefficients.

In questa Nota si studiano operatori della forma $A u = - △ u + (\nabla F, \nabla u)$ in $L_{μ}^{2} (R^{n})$ con $d μ (x) = e^{- F (x)} d x$ , e operatori di Schrödinger in $L^{2} (R^{n})$ . 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.

Publié le : 2000-03-01

MR 1797049 | Zbl 0982.35078

@article{RLIN_2000_9_11_1_9_0,
     author = {Giorgio Metafune and Diego Pallara},
     title = {Discreteness of the spectrum for some differential operators with unbounded coefficients in \( \mathbb{R}^{n} \)},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {11},
     year = {2000},
     pages = {9-19},
     zbl = {0982.35078},
     mrnumber = {1797049},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_2000_9_11_1_9_0}
}

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. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 11 (2000) pp. 9-19. http://gdmltest.u-ga.fr/item/RLIN_2000_9_11_1_9_0/

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