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One-Dimensional Schrödinger Operators with Complex Potentials
Annales Henri Poincaré ( IF 1.4 ) Pub Date : 2020-02-17 , DOI: 10.1007/s00023-020-00901-9
Jan Dereziński , Vladimir Georgescu

We discuss realizations of \(L:=-\partial _x^2+V(x)\) as closed operators on \(L^2]a,b[\), where V is complex, locally integrable and may have an arbitrary behavior at (finite or infinite) endpoints a and b. The main tool of our analysis is Green’s operators, that is, various right inverses of L.

中文翻译:

具有复数势的一维Schrödinger算子

我们将\(L:=-\ partial _x ^ 2 + V(x)\)的实现作为\(L ^ 2] a,b [\)上的封闭算符进行讨论,其中V是复杂的,局部可积分的并且可能具有在(有限或无限)端点ab处的任意行为。我们分析的主要工具是Green的运算符,即L的各个右逆。
更新日期:2020-02-17
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