@article {Berti2013229,
	title = {Quasi-periodic solutions with Sobolev regularity of NLS on Td with a multiplicative potential},
	journal = {Journal of the European Mathematical Society},
	volume = {15},
	number = {1},
	year = {2013},
	note = {cited By (since 1996)5},
	pages = {229-286},
	abstract = {We prove the existence of quasi-periodic solutions for Schr{\"o}dinger equations with a multiplicative potential on Td , d >= 1, finitely differentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are C$\infty$ then the solutions are C$\infty$. The proofs are based on an improved Nash-Moser iterative scheme, which assumes the weakest tame estimates for the inverse linearized operators ("Green functions") along scales of Sobolev spaces. The key off-diagonal decay estimates of the Green functions are proved via a new multiscale inductive analysis. The main novelty concerns the measure and "complexity" estimates. {\textcopyright} European Mathematical Society 2013.},
	issn = {14359855},
	doi = {10.4171/JEMS/361},
	author = {Massimiliano Berti and Philippe Bolle}
}
