TY - RPRT

T1 - Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator

A1 - Jensen,Arne

A1 - Yajima,Kenji

AU - Jensen,Arne

AU - Yajima,Kenji

PB - Department of Mathematical Sciences, Aalborg University

PY - 2009

Y1 - 2009

N2 - We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials, which grow at spatial infinity slower than quadratic, but faster than linear functions, and whose Hessian matrices have a fixed sign. We prove that the fundamental solution at resonant times grows indefinitely at spatial infinity with the algebraic growth rate, which increases indefinitely, when the growth rate of perturbations at infinity decrease from the near quadratic to the near linear ones.

AB - We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials, which grow at spatial infinity slower than quadratic, but faster than linear functions, and whose Hessian matrices have a fixed sign. We prove that the fundamental solution at resonant times grows indefinitely at spatial infinity with the algebraic growth rate, which increases indefinitely, when the growth rate of perturbations at infinity decrease from the near quadratic to the near linear ones.

BT - Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator

T3 - Research Report Series

T3 - en_GB

ER -