电荷转移模型的精细性质
Fine properties of Charge Transfer Models
摘要：
我们证明了当n >或= 3时，R^n中电荷转移哈密顿量H（t）的L ^1到L^infinity估计，然后讨论了同一模型从W^{k，p '}到W^{k，p}的估计，其中2 < p < infinity，1/p + 1/p'= 1。然后，利用几何方法建立了电荷转移算子演化的H^k范数的时间有界性和Hamilton算子H（t）在H^k范数下的渐近完备性，其中k为任意正整数.
英文摘要：
We prove L^1 to L^infinity estimates for charge transfer Hamiltonians H(t) in R^n for n > or = 3, followed by a discussion of estimates from W^{k,p'} to W^{k,p} for the same model, where 2 < p < infinity and 1/p + 1/p'=1. Then, geometric methods are developed to establish the time boundedness of the H^k norm for the evolution of charge transfer operators and asymptotic completeness of the Hamiltonian H(t) in the H^k norm, where k is any positive integer.
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