关于直和空间上算子的谱分解问题

将针对两个Ｈｉｌｂｅｒｔ空间的直和空间上的算子讨论其谱分解问题，这类问题在目前文献中讨论的还不很多，这里将解决如下三个问题：两个对称算子的谱与它的直和算子的谱之间的关系；通过两佧自伴算子的谱分解直接得到其直和算子的谱分解，常型直和空间上自伴的Ｓｔｕｒｍ－Ｌｉｏｕｖｉｌｌｅ算子的特征展开及谱分解。

Spectral Decomposition of Operators in Direct Sum Spaces

pectral decomposition of operators in direct sum space of two Hilbert spaces is discussed. Onthis problem there are few discussions in current literature. Here, the following results are ob-tained: the relationship between the spectrums of two symmetrical operators and the spectrum oftheir direct sum operator is made clear; the spectral decomposition of direct sum operator is givenby the spectral decompositions of two self adjoint operators; the characteristic expansion and spec-tral decomposition of self-adjoint Sturm-Liouville operators in direct sum spaces of finite intervalsare obtained. Some of the results in this paper can be extended to direct sum space of more than twoHilbert spaces.