[1]杨传富*,王於平.四阶极限点型微分算子积的自伴边值问题[J].南京理工大学学报(自然科学版),2005,(01):116-118.
 YANG Chuan-fu,WANG Yu-ping.Self-adjoint Boundary Value for Products of Limit-point Fourth-order Differential Operators[J].Journal of Nanjing University of Science and Technology,2005,(01):116-118.
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四阶极限点型微分算子积的自伴边值问题
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《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

卷:
期数:
2005年01期
页码:
116-118
栏目:
出版日期:
2005-02-28

文章信息/Info

Title:
Self-adjoint Boundary Value for Products of Limit-point Fourth-order Differential Operators
作者:
杨传富1* 王於平2
1. 南京理工大学理学院, 江苏南京210094;
2. 南京林业大学信息学院, 江苏南京210037
Author(s):
YANG Chuan-fu1WANG Yu-ping2
1.School of Sciences, NUST, Nanjing 210094, China; 2.College of Information Science and Technology, Nanjing Forest University, Nanjing 210037, China
关键词:
极限点型微分算式 自伴算子 微分算子积
Keywords:
lim i-t po in t d ifferent ial expression se l-f ad jo int operato r products of differentia l operators
分类号:
O175.3
摘要:
在微分算式l(y)=y(4) -(py′)′+qy(t∈ [a,∞ ) )满足lk(y) (k=1,2)均为极限点型条件下,该文运用Calkin定理及微分算子自伴扩张理论,以边界条件形式研究了由l(y)生成的 2个微分算子积的自伴边值问题,并获得其自伴的充分必要条件,其结果对微分算子理论的研究是有益的。
Abstract:
For the d ifferentia l expression l (y ) = y ( 4) - (pyc) c+ qy, tI [ a, ] ), under the assumpt ion that l k (y ) ( k= 1, 2) is lim i-t po in,t employ ing C alk in. s theorem and the theory o f sel-f adjoint ex tensions of di-f ferent ial operators, w e investigated the sel-f ad jo intness of product operator L2L1 where Li ( i= 1, 2) are generated by l (y ) w ith some boundary cond itions. A necessary and suffic ient cond ition for se l-f ad jo intness o f L2L1 w as obtained by boundary condit ions. This result is useful in theory o f the d ifferentia l operators

参考文献/References:

[ 1] C ao Zh ijiang, Sun Jiong, Edm unds D E. On se l-f adjo in-t ness o f the product o f two second-orde r d ifferentia l operato rs [ J]. Ac taM ath. S in ica( English Ser ies), 1999, 15 ( 3): 375- 386.
[ 2] K auffm an R, Read T, Zettl A. The defic iency index problem of powe rs of ord inary differential expressions [M ]. New York: Springer-Ver lag, 1977.
[ 3] Na im ark M A. L inear d iffe rentia l operators [M ]. New York: Freder ick Ungar Publish ing Co, 1968.
[ 4] 刘景麟. 对称算子自伴延拓的Ca lk in描述[ J]. 内蒙古大学学报(自然科学版), 1988, 19( 4): 573- 587.
[ 5] Sun Jiong. On the sel-f ad jo int extensions of symm etric o rd ina ry differentia l operatorsw ithm iddle deficiency ind ices [ J]. Acta M a th. S in ica ( New Series), 1986, 2 ( 2 ): 152- 167.
[ 6] 曹之江. 常微分算子[M ]. 上海: 上海科学技术出版社, 1987.

相似文献/References:

[1]王於平.一类4阶微分算子积的自伴性[J].南京理工大学学报(自然科学版),2003,(06):738.
 Wang Yuping.On Self-adjointness of Product of Two Fourth-order Differential Operators[J].Journal of Nanjing University of Science and Technology,2003,(01):738.

备注/Memo

备注/Memo:
作者简介: 杨传富( 1968- ), 男, 安徽六安人, 博士生, 主要研究方向: 泛函分析及微子算子理论, E-ma il:chuanfuyang@ tom. com。
更新日期/Last Update: 2013-03-03