期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

两个四阶微分算子积的自伴性 被引量：7

Self-adjointness of Product of Two 4th-order Differential Operators
下载PDF
导出
摘要 本文研究由微分算式D^4-DpD+q生成的两个四阶微分算子L_i(i=1,2)的积L_2L_1的自伴性,并在常型和奇型情形下,分别获得了两个四阶微分算子积自伴的充要条件,同时证明了若L_1和L_2自伴,则L=L_2L_1自伴的充要条件是L_1=L_2。 In this paper, we study the self-adjointness of product L_2L_1 of two 4th-order differential operators L_i(i=1, 2) generated by the diffrential expression D^4--DpD+q and obtain a necessary and sufficient condition for the self-adjoininess of product of two 4th-order differential operators, respectively, when both I=[a, b]and [0, ∞]. We prove that if both L_1 and L_2 are self-adjoint, then L=L_2L_1 is self-adjoint if and only if L_1=L_2.
作者 杨传富 黄振友 杨孝平
机构地区 南京理工大学理学院应用数学系
出处 《数学进展》 CSCD 北大核心 2004年第3期291-302,共12页 Advances in Mathematics（China）
关键词 自伴算子 两个微分算子积 边条件 self-adjoint operator product of two differential operators boundary conditions
分类号 O175.3 [理学—基础数学]
  • 相关文献

参考文献11

  • 1Cao Zhijiang. Ordinary Differential Operators [M] (In Chinese). Shanghai: Shanghai Sinence and Technology Press, 1986.
  • 2Cao Zhijiang, Sun Jiong, Edmunds D E. On self-adjointness of the product of two second-order differential operators [J]. Acta Math. Sinica (English Series), 1999, 15(3): 375-386.
  • 3Cao Zhijiang, Liu Jinglin. On the deficiency index theory of singular symmetric differential operators [J].(In Chinese), Beijing: Advance in Math., 1983, 12(3): 161-178.
  • 4Coddington E A. The spectral representation of ordinary self-adjoint differential operators [J]. An. Math.,1954, 60(1): 192-211.
  • 5Edmunds D E, Evans W D. Spectral Theory and Differential Operators [M]. Oxford: Oxford University Press, 1987.
  • 6Kauffman R, Read T, Zettl A. The Deficiency Index Problem of Powers of Ordinary Differential Expressions[M]. Lect. Notes in Math. 621, Berlin, New York: Springer-Verlag, 1977.
  • 7Liu Jinglin. On the Calkin approach of self-adjoint extensions of symmetric operators [J]. (in Chinese), J Inner Mongolia University, 1988, 19(4): 573-587.
  • 8Naimark N A. Linear Differential Operators [M]. Vol. Ⅱ, Ungar, New York, 1968.
  • 9Race D, Zettl A. On the commutativity of certain quasi-differential expression I [J]. J London Math. Soc.,1990, 42(2): 489-504.
  • 10Sun Jiong. On the self-adjoint extensions of symmetric ordinary differential operators with middle deficiency indices [J]. Acta Math. Sinica (New Series), 1986, 2(2): 152-167.

同被引文献32

引证文献7

二级引证文献5

数学进展
2004年 第3期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部