Uniqueness of the interior transmission problem with partial information on the potential and eigenvalues

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• 作者：Chuan-Fu Yang^a ; ¹ ; ^{chuanfuyang@njust.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Sergey Buterin^b ; ¹ ; ^{buterinsa@info.sgu.ru" class="auth_mail" title="E-mail the corresponding author}
• 关键词：34A55 ; 34L40 ; 35R30 ; 35Q60 ; 35J40
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：15 March 2016
• 年：2016
• 卷：260
• 期：6
• 页码：4871-4887
• 全文大小：308 K

文摘

The inverse spectral problem of determining a spherically symmetric wave speed v is considered in a bounded spherical region of radius b. A uniqueness theorem for the potential q   of the derived Sturm–Liouville problem B(q)$B(q)$ is presented from the data involving fractions of the eigenvalues of the problem B(q)$B(q)$ on a finite interval and knowledge of q over a corresponding fraction of the interval. The methods employed rest on Weyl-function techniques and properties of zeros of a class of entire functions.