hal-00368072, version 1
Exponential decay of eigenfunctions of first order systems
Adventures in mathematical physics American Mathematical Society (Ed.) (2007) 249-256
Résumé : The author studies exponential decay of the eigenfunctions of first-order (matrix) differential operators of the form $$ H = -i \sum_{j=1}^d A_j \frac{\partial}{\partial x_j} + V(x). $$ It is shown that under certain assumptions, the eigenfunctions obey estimates of the type $$ \int_{\Bbb R^d} |\psi(x)|^2 e^{2\delta x} \, dx < \infty. $$ The author emphasizes that these estimates are valid everywhere off the essential spectrum $\sigma_{\rm ess}$, not just below the minimum of $\sigma_{\rm ess}$.
- 1 :
- CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne
- Domaine : Mathématiques/Equations aux dérivées partielles
- Commentaire : Papers from the International Conference on Transport and Spectral Problems in Quantum Mechanics held in honor of Jean-Michel Combes at the Université de Cergy-Pontoise – Cergy-Pontoise – September 4--6 – 2006
- hal-00368072, version 1
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- Soumis le : Vendredi 13 Mars 2009, 15:10:50
- Dernière modification le : Mardi 12 Juin 2012, 17:35:41
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