Riemannian Manifolds With Uniformly Bounded Eigenfunctions
Toth, John ; Zelditch, Steve
arXiv, 0002038 / Harvested from arXiv
Text on arXiv
The standard eigenfunctions $\phi_{\lambda} = e^{i < \lambda, x >}$ on flat tori $\R^n / L$ have $L^{\infty}$-norms bounded independently of the eigenvalue. In the case of irrational flat tori, it follows that $L^2$-normalized eigenfunctions have uniformly bounded $L^{\infty}$-norms. Similar bases exist on other flat manifolds. Does this property characterize flat manifolds? We give an affirmative answer for compact Riemannian manifolds with completely integrable geodesic flows.
Publié le : 2000-02-15
Classification:  Mathematical Physics,  Mathematics - Spectral Theory,  81Qxx 
@article{0002038,
     author = {Toth, John and Zelditch, Steve},
     title = {Riemannian Manifolds With Uniformly Bounded Eigenfunctions},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0002038}
}

Toth, John; Zelditch, Steve. Riemannian Manifolds With Uniformly Bounded Eigenfunctions. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0002038/