A new approach to inverse spectral theory
A new approach to inverse spectral theory
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发表时间：
2016
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通讯作者：
B. Simon
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作者：
B. Simon
We present a new approach (distinct from Gel'fand-Levitan) to the theorem of Borg-Marchenko that the m-function (equivalently, spectral measure) for a finite interval or half-line Schr6dinger operator determines the potential. Our approach is an analog of the continued fraction approach for the moment problem. We prove there is a representation for the m-function m(-n2) = -/ - 0bA(a)e-2ada + O(e-(2b-6)). A on [0,a] is a function of q on [0, a] and vice-versa. A key role is played by a differential equation that A obeys after allowing x-dependence: aA _A o a
