Reflectionless Analytic Difference Operators III. Hilbert Space Aspects
Reflectionless Analytic Difference Operators III. Hilbert Space Aspects
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无反射解析差分算子 III。
DOI：
10.2991/jnmp.2002.9.2.4
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发表时间：
2002
影响因子：
0.7
通讯作者：
S. Ruijsenaars
中科院分区：
文献类型：
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作者：
S. Ruijsenaars
在本系列论文的前两部分中，我们介绍和研究了一类含有无反射本征函数的解析差分算子，第一部分着重于代数和泛函理论的特征，第二部分着重于与孤子的联系。在第三部分中，我们从量子力学的角度研究我们的差分算子。特别地，我们证明了对于来自某个子类的任意差分算子A，无反射A-本征函数可以用来构造L2（λ，dx）上的无界自伴无反射算子，其在适当核上的作用与A的作用一致.
Abstract In the previous two parts of this series of papers, we introduced and studied a large class of analytic difference operators admitting reflectionless eigenfunctions, focusing on algebraic and function-theoretic features in the first part, and on connections with solitons in the second one. In this third part we study our difference operators from a quantum mechanical viewpoint. We show in particular that for an arbitrary difference operator A from a certain subclass, the reflectionless A-eigenfunctions can be used to construct an unbounded self-adjoint reflectionless operator  on L 2(ℝ, dx), whose action on a suitable core coincides with that of A.