Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter

• Autoři: ZEMÁNEK Petr
• Rok publikování: 2021
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Journal of Mathematical Analysis and Applications
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://doi.org/10.1016/j.jmaa.2021.125054
• Doi: https://doi.org/10.1016/j.jmaa.2021.125054
• Klíčová slova: Discrete symplectic system; Eigenvalue; Eigenfunction; Expansion theorem; M(lambda)-function
• Popis: Eigenfunctions expansion for discrete symplectic systems on a finite discrete interval is established in the case of a general linear dependence on the spectral parameter as a significant generalization of the Expansion theorem given by Bohner et al. (2009) [14]. Subsequently, an integral representation of the Weyl-Titchmarsh M(lambda)-function is derived explicitly by using a suitable spectral function and a possible extension to the half-line case is discussed. The main results are illustrated by several examples.

Související projekty

• Nová oscilační teorie pro lineární hamiltonovské a symplektické systémy