The Spectram Of Hamiltonian Operator Matrics Corresponding To Partial Differential Equation

In this thesis,we mainly study the spectrum of Hamilton operator matrics corresponding to partial differential equation with certain boundary conditions based on pseudo division. If some proper domains are given to the matrics, there will be some obvious result about the spectrum. On one side,we investigate the partial differential equation including three and six terms,then some conclusions are obtained ,and they have close relation with the type of the equation,orΔ= a₁₂² - a₁₁a₂₂. Acorrding to this and some important coefficients,we conclude the results. They are important to the spectrum and general results .On the other side,we make the conclusion that some Hamilton operator matrics are similar in proper condition and special domain,this thesis mainly concerns the similarity of diag-onal,lower triangular Hamilton operator matrics. Then we discuss the similarity of different operator matrics when their skew diagonal operators are exchanged. And specific examples are shown to illastrate the effectiveness of the obove conclusions. It makes another step to the field of relationlship between Hamilton operator matrics.