A note on relative oscillation theory for symplectic difference systems with general boundary conditions

作者：Elyseeva Julia^*

来源：Applied Mathematics Letters, 2012, 25(11): 1809-1814.

DOI：10.1016/j.aml.2012.02.024

• Discrete eigenvalue problem
• Symplectic difference system
• Relative oscillation theory
• Comparative index

We develop an analog of classical oscillation theory for discrete symplectic eigenvalue problems with general self-adjoint boundary conditions which, rather than measuring of the spectrum of one single problem, measures the difference between the spectra of two different problems. We prove formulas connecting the numbers of eigenvalues in a given interval for two symplectic eigenvalue problems with different self-adjoint boundary conditions. We derive as corollaries generalized interlacing properties of eigenvalues.

• 出版日期2012-11