The Spectral Theory Of Linear Operator And Its Application

The spectral theory of the linear operator occupies an important position in the functional analysis. Firstly, in this paper, we introduced the traditional classifications and properties of spectrum. And we gave a lot of examples to demonstrate how to calculate the spectrum. For example, the multiplication operator, integral operator, differential operator and translation operator. Secondly, we introduced a series of non-traditional spectrums,such as essential spectrum, approximate spectrum, etc. According to certain standard, we gave a new way of classification in the spectrum. Thirdly, as an important part of spectral theory of the linear operator, we also introduced the spectral mapping theory of Banach algebra, linear operator and semigroup. Lastly, as an application, we talked about spectral analysis of stability based on the wave system with boundary feedback control.