Metafune, Pallara: Discreteness of the spectrum for some differential operators with unbounded coefficients in \( \mathbb{R}^{n} \)

Metafune, Giorgio and Pallara, Diego:
Discreteness of the spectrum for some differential operators with unbounded coefficients in \( \mathbb{R}^{n} \) (Proprietà di spettro discreto per operatori differenziali con coefficienti illimitati in \( \mathbb{R}^{n} \))
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 11 (2000), fasc. n.1, p. 9-19, (English)
pdf (380 Kb), djvu (170 Kb). | MR1797049 | Zbl 0982.35078

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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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Referenze Bibliografiche