科研之友
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摘要
We show that a lattice Schrodinger operator Delta + v acting in C-Zd does not have l(2) eigen-functions if its potential v(center dot) admits fast local approximation by periodic functions. A special case of this result states that if v(x) = V(alpha(1)x(1), ..., a(d)x(d)), where V(center dot) is a (1, ... , 1)periodic function on R-d satisfying the Holder condition and (alpha(1), ... , alpha(d)). Rd is a vector admitting fast rational approximation, then the operator Delta + v has no eigenfunctions in l(2)(Z(d)). The one-dimensional case of this statement has been known since 1970s, and the question whether its multidimensional generalization was possible remained open since then.
- 出版日期2017-5
