Linear operators associated with differential and difference systems: What is different?
|Druh||Článek ve sborníku|
|Konference||Progress on Difference Equations and Discrete Dynamical Systems. ICDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 341|
|Fakulta / Pracoviště MU|
|Klíčová slova||discrete symplectic system; linear Hamiltonian differential system; linear relations; multi-valuedness; densely defined operator; time scale|
|Popis||The existence of a densely defined operator associated with (time-reversed) discrete symplectic systems is discussed and the necessity of the development of the spectral theory for these systems by using linear relations instead of operators is shown. An explanation of this phenomenon is provided by using the time scale calculus. In addition, the density of the domain of the maximal linear relation associated with the system is also investigated.|