形式自伴差分方程的正负亏指数
The positive and negative deficiency indices of formally self-adjoint difference equations
摘要：
本文研究形式自伴差分方程及其正负亏指数。证明了形式自伴差分方程的阶是偶数，并给出了形式自伴差分方程的一些特征。进一步证明了正亏指数和负亏指数总是相等的，这意味着由差分方程生成的极小线性关系的自伴扩张的存在性.这是形式自伴差分方程与谱理论中相应的微分方程之间的一个重要而本质的区别。
英文摘要：
This paper is concerned with formally self-adjoint difference equations and their positive and negative deficiency indices. It is shown that the order of any formally self-adjoint difference equation is even, and some characterizations of formally self-adjoint difference equations are established. Further, we show that the positive and negative deficiency indices are always equal, which implies the existence of the self-adjoint extensions of the minimal linear relations generated by the difference equations. This is an important and essential difference between formally self-adjoint difference equations and their corresponding differential equations in the spectral theory.
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