Regularity and decay of solutions of nonlinear harmonic oscillators |
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Authors: | Marco Cappiello Fabio Nicola |
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Institution: | 1. Dipartimento di Matematica, Università degli Studi di Torino, Via Carlo Alberto 10, 10123 Torino, Italy;2. Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy |
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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 . Our results apply, in particular, to nonlinear eigenvalue problems for the harmonic oscillator associated to a real-analytic scattering, or asymptotically conic, metric in , as well as to certain perturbations of the classical harmonic oscillator. |
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Keywords: | Nonlinear harmonic oscillators Holomorphic extension Gaussian decay Pseudodifferential operators |
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