THE INVERSE PROBLEM FOR A SPECTRAL ASYMMETRY FUNCTION OF THE SCHRÖDINGER OPERATOR ON A FINITE INTERVAL
THE INVERSE PROBLEM FOR A SPECTRAL ASYMMETRY FUNCTION OF THE SCHRÖDINGER OPERATOR ON A FINITE INTERVAL
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DOI：
10.1112/mtk.12105
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发表时间：
2020-09
期刊：
影响因子：
0.8
通讯作者：
Malcolm Brown;K. Schmidt;S. Shipman;I. Wood
中科院分区：
文献类型：
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作者：
Malcolm Brown;K. Schmidt;S. Shipman;I. Wood
对于薛定谔方程$-d^2 u/dx^2 + q（x）u = \lambda u$在有限x$-区间上，定义了一个“非对称函数”$a（\lambda;q）$，它是1/2阶整的，类型为1。我们的主要结果确定类的平方可积的潜力$q（x）$具有一个共同的不对称功能。对于任何给定的$a（\lambda）$，每个Dirichlet谱序列都有一个势能。
For the Schrodinger equation $-d^2 u/dx^2 + q(x)u = \lambda u$ on a finite $x$-interval, there is defined an "asymmetry function" $a(\lambda;q)$, which is entire of order $1/2$ and type $1$ in $\lambda$. Our main result identifies the classes of square-integrable potentials $q(x)$ that possess a common asymmetry function. For any given $a(\lambda)$, there is one potential for each Dirichlet spectral sequence.