理论数学

Vol.9 No.3 (May 2019)

Hochstadt-Lieberman定理的重构问题
The Reconstructing Problem for Hochstadt-Lieberman Theorem

 

作者:

曾献清 , 魏朝颖 , 郭 洁 :西安石油大学理学院,陕西 西安

 

关键词:

特征值Mittag-Leffler展开定理Levin-Lyubarski插值重构问题Eigenvalue Mittag-Leffler Expansion Theorem Levin-Lyubarski Interpolation Reconstruction Problem

 

摘要:

Hochstadt-Lieberman唯一性定理表明,对于定义在[0, 1]区间上的Sturm-Liouville问题,若[0, 1/2]区间上的势函数已知,则一组Dirichlet-Dirichlet特征值即可唯一确定整个区间上的势函数。本文应用亚纯函数的Mittag-Leffler展开定理,给出了重构该问题势函数的一种新方法,同时给出了该问题的解存在的充要条件。

In this paper we are concerned with the Hochstadt-Lieberman uniqueness theorem which states that, when the potential is known a priori on [0, 1/2], the full Dirichlet-Dirichlet spectrum of a Sturm-Liouville problem defined on the interval [0, 1] uniquely determines its potential. We shall give a new method for reconstructing the potential for this problem in terms of the Mittag-Leffler decomposition Theorem of meromorphic functions associated with the solution of Sturm-Liouville equantions. We also give a necessary and sufficient condition for the existence of the solution.

文章引用:

曾献清 , 魏朝颖 , 郭 洁 (2019) Hochstadt-Lieberman定理的重构问题。 理论数学, 9, 458-464. doi: 10.12677/PM.2019.93061

 

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