一类色散半群的基本估计

Basic Estimates for a Class of Dispersive Semigroups

本文通过Zhang得到的估计振荡积分方法研究了色散半群 F−1ei[xξ+(ξn+ξ)t]F 在n 为奇数且有界时的一维衰减估计问题, 展示了该振荡积分估计方法在研究半群衰减问题中的重要性.

In this paper, we study the problem of one-dimensional attenuation estimation of dis-persion semigroups F−1ei[xξ+(ξn+ξ)t]F when n is odd and bounded by using the estimated oscillatory integration method obtained by Zhang. The importance of the estimated oscillatory integration method in the study of semigroup attenuation is demonstrated.