The dependence of radiation damping on the space dimension

The model of an interacting oscillator-field-system is discussed and the dependence of the asymptotic behavior of the oscillator on the space-dimension is investigated. It turns out that in spaces with odd dimension n >= 3 the amplitude of the oscillator tends faster to zero than any power of 1/t for t → infinity. In spaces with even dimension n >= 4 it tends to zero as approximately tsup(1-n). (Auth.)