Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6426026 | Advances in Mathematics | 2012 | 34 Pages |
Abstract
We prove sharp analytic regularity and decay at infinity of solutions of variable coefficients nonlinear harmonic oscillators. Namely, we show holomorphic extension to a sector in the complex domain, with a corresponding Gaussian decay, according to the basic properties of the Hermite functions in Rd. Our results apply, in particular, to nonlinear eigenvalue problems for the harmonic oscillator associated to a real-analytic scattering, or asymptotically conic, metric in Rd, as well as to certain perturbations of the classical harmonic oscillator.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Marco Cappiello, Fabio Nicola,