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高阶加权微分算子谱的离散性 被引量：1

DISCRETENESS OF SPECTRA OF HIGH ORDER DIFFERENTIAL OPERATORS WITH WEIGHTED FUNCTIONS
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摘要 本文研究了加权的高阶微分算子的谱. 利用分解的方法和不等式的估计, 得到了一些高阶对称微分算子的任何自共轭扩张的谱离散的充分条件, 推广了 Pfeiffer , Sun, Glazman 等人的结果,利用这些结果可以判别某些微分算子谱的离散性. The investigations deal with the spectra of high order differential operators with weighted functions.Using the method of decomposition and the estimate of inequalities,we obtain the spectra of all the self-adjoint extensions of high order symmetric differential operators are discrete under certain conditions on the coefficients.Our results extend the results of Mller Pfeiffer E.,Sun Jiong and Glazman.Using the results obtained,we can easily judge the discreteness of spectra of some differential operators.
作者 张茂柱 孙炯 敖继军
机构地区 内蒙古大学数学科学学院 泰山学院数学与系统科学学院 内蒙古工业大学理学院
出处 《数学杂志》 CSCD 北大核心 2012年第2期331-338,共8页 Journal of Mathematics
基金 国家自然科学基金资助项目 (10861008 11161030)
关键词 微分算子 离散谱 权函数 differential operators discrete spectrum weighted functions
分类号 O175.3 [理学—基础数学]
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参考文献11

  • 1Read T T. Positivity and discrete spectra for di?erential operators[J]. J. Di?. Equat.,1982,43(1): 1-27.
  • 2Edmunds D E,Sun Jiong. Embedding theorems and the spectra of certain di?erential operators[J]. Proc. Roy. Soc. Lond. A,1991,434: 643-656.
  • 3Hinton D B,Lewis R T. Singular di?erential operators with spectra discrete and bounded below[J]. Proc. Roy. Soc. Edinburgh A,1979,84: 117-134.
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  • 9孙炯,王忠.常微分算子谱的定性分析[J].数学进展,1995,24(5):406-422. 被引量：31
  • 10Lewis R T. The discreteness of the spectrum of self-adjoint,even order,one term di?erential operators[J]. Proc. Amer. Math. Soc.,1974,42(2): 480-482.

二级参考文献4

  • 1Cowen Carl C, MacCluer Barbara D. Composition operators on spaces of analytic functions[M]. Studies in Advanced Mathematics. Boca Raton, FL: CRC Press, 1995.
  • 2Zhu Kehe. Operator theory in function spaces[M]. Pure and Applied Mathematics, Vol. 139. New York, Basel: Marcel Dekker Inc., 1990.
  • 3Hibschweiler R A, Portnoy N. Composition followed by differentiation between Bergman and Hardy spaces[J]. Rocky Mountain J. Math., 2005, 35(3): 843-855.
  • 4Ohno S . Products of composition and differentiation between Hardy spaces[J]. Bull. Austral. Math. Soc., 2006, 73(2): 235-243.

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数学杂志
2012年 第2期

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