Eigenvalues of periodic Sturm Liouville problems

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• 作者：Yaping Yuan^a ; ^{yaping_yyp@qq.com} ; Jiong Sun^a ; ^{272454707@qq.com} ; Anton Zettl^b ; ^{zettl@msn.com}
• 关键词：primary ; 34B20 ; 34B24 ; secondary ; 47B25
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：517
• 期：Complete
• 页码：148-166
• 全文大小：378 K
• 卷排序：517

文摘

For h-periodic coefficients and any integer k>2 it is well known that the eigenvalues of some self-adjoint complex boundary condition on the interval [a,a+h][a,a+h] are the same as the periodic eigenvalues on the interval [a,a+kh][a,a+kh]. For each k we identify explicitly which of the uncountable number of complex conditions generates these periodic eigenvalues. In addition, we prove an analogous result for semi-periodic eigenvalues.