@inbook{74b451e8aea44384b550e72af88bcd78,

title = "Wiener randomization on unbounded domains and an application to almost sure well-posedness of NLS",

abstract = "We consider a randomization of a function on ℝ^d that is naturally associated to the Wiener decomposition and, intrinsically, to the modulation spaces. Such randomized functions enjoy better integrability, thus allowing us to improve the Strichartz estimates for the Schr{\"o}dinger equation. As an example, we also show that the energy-critical cubic nonlinear Schr{\"o}dinger equation on ℝ^4 is almost surely locally well-posed with respect to randomized initial data below the energy space. ",

keywords = "nonlinear Schr{\"o}dinger equation, almost sure well-posedness, modulation space, Wiener decomposition, Strichartz estimate, Fourier restriciton norm method",

author = "Arpad Benyi and Tadahiro Oh and Oana Pocovnicu",

year = "2015",

month = oct,

doi = "10.1007/978-3-319-20188-7",

language = "English",

isbn = "978-3-319-20187-0",

volume = "4",

series = "Applied and Numerical Harmonic Analysis",

publisher = "Basel: Birkhauser Verlag",

pages = "3--25",

editor = "R. Balan and M. Begue and J.J. Benedetto and Czaja, {W. } and K.A. Okoudjou",

booktitle = "Excursions in Harmonic Analysis",

}