| 高云兰;王 忠;吴宏友.自共轭算子束的谱及其应用[J].数学年刊A辑,2012,33(1):101~ |
| 自共轭算子束的谱及其应用 |
| Spectra of Self-adjoint Operators Pencil and Its Applications |
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| DOI： |
| 中文关键词: 谱, 本质谱, 谱曲线, 特征曲线, 特征值 |
| 英文关键词:Spectrum, Essential spectrum, Spectral curve, Eigen-curve, Eigenvalues |
| 基金项目: |
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| 中文摘要: |
| 首先研究了自共轭算子束$L-\lambda V$的谱曲线, 其中$L$ 和$V$是Hilbert空间$H$内的自共轭算子. 其次研究了谱问题$Ly=\lambdaVy$的特征值.最后, 将所得的结论应用到正则和奇异的常微分算子的不定谱问题中. |
| 英文摘要: |
| In this paper, the authors first study the spectral curves of aself-adjoint operators pencil $L-\lambda V$, where $L$ and $V$ areself-adjoint operators in a Hilbert space $H$. Second, theeigenvalues of spectral problem $Ly=\lambda Vy$ are studied. Finally, the authors apply these results to the so-called indefinite spectralproblems for ordinary differential operators which are both regularand singular. |
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