2n阶线性q-差分方程的奇异边值问题的谱理论  

On Spectral Theory of Singular Boundary Value Problems of 2n-th Order Linear q-Difference Equations

作　　者：吕亚丹 

机构地区：[1]天津大学理学院,天津300072

出　　处：《西南师范大学学报（自然科学版）》2015年第3期11-17,共7页Journal of Southwest China Normal University(Natural Science Edition)

摘　　要：主要考虑2n阶线性q-差分方程的奇异边值问题.首先证明了奇异边值问题中的差分算子所对应的积分算子是线性自共轭全连续算子,然后利用线性自共轭全连续算子的谱理论给出了2n阶线性q-差分方程的奇异边值问题的谱性质.In this paper ,the singular boundary value problems of 2n_th order liner q_difference equations have been studied .It has been proved that the corresponding resolvent operator of the q_difference operator is a linear self_adjoint completely continuous difference operator .The spectrum of the singular boundary value problems of the 2n_th order liner q_difference equations has been obtained by means of the spectral theory of linear self_adjoint completely continuous operator .

关 键 词：奇异边值问题 谱理论 自共轭算子 紧性 

分 类 号：O175[理学—数学]