极限点型 Sturm-Liouville 算子乘积的自伴性

杨传富

系统科学与数学 ›› 2006, Vol. 26 ›› Issue (3) : 368-374.

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系统科学与数学 ›› 2006, Vol. 26 ›› Issue (3) : 368-374. DOI: 10.12341/jssms09207
论文

极限点型 Sturm-Liouville 算子乘积的自伴性

    杨传富
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Self-Adjointness Of Products Of The Limit-Point Sturm-Liouville Operators

    Yang Chuanfu
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文章历史 +

摘要

假设微分算式 l(y)=(py)+qy, t[a,), 满足 lk(y) (k=1,2,3) 均为极限点型,作者研究了由 l(y) 生 成的两个微分算子 Li (i=1,2) 的乘积 L2L1 的自伴性问题并获得其自伴的充分必要条件. 同时研究了由 l(y)=y+qy, t[a,), 生成的三个微分算子 Li (i=1,2,3) 的 乘积 L3L2L1 的自伴性问题.

Abstract

For the differential expression l(y)=(py)+qy, t[a,), under the assumption that lk (k=1,2,3) are limit-pointed, the author studies the self-adjointness of the product operator L2L1, which Li (i=1,2) are generated by l(y), and obtains a necessary and sufficient condition for self-adjointness of L2L1. Also, a necessary and sufficient condition for the self-adjointness of L3L2L1, which Li (i=1,2,3) are associated with l(y)=y+qy, t[a,), is obtained.

关键词

微分算子乘积 / 极限点型微分算式 / 自伴边界

Key words

Products of differential operators / limit-pointed differential expression / self-adjoint boundary con

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杨传富. 极限点型 Sturm-Liouville 算子乘积的自伴性. 系统科学与数学, 2006, 26(3): 368-374. https://doi.org/10.12341/jssms09207
Yang Chuanfu. Self-Adjointness Of Products Of The Limit-Point Sturm-Liouville Operators. Journal of Systems Science and Mathematical Sciences, 2006, 26(3): 368-374 https://doi.org/10.12341/jssms09207
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