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The characteristic matrix function of a dissipative Hamiltonian operator
Author(s) -
Uğurlu Ekin
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6834
Subject(s) - dissipative operator , mathematics , dissipative system , operator (biology) , hamiltonian (control theory) , pure mathematics , resolvent , matrix function , finite rank operator , mathematical analysis , algebra over a field , eigenvalues and eigenvectors , symmetric matrix , quantum mechanics , physics , mathematical optimization , biochemistry , chemistry , repressor , transcription factor , gene , banach space
In this paper, we consider a singular dissipative even‐order Hamiltonian operator with a finite number of transmission conditions. Using coordinate‐free approach, we construct the characteristic matrix‐function of the Cayley transform of the dissipative operator. Using the equivalence of completeness property of root functions of Cayley transform and dissipative operator, we prove some completeness theorems. Moreover, we construct an explicit form of the resolvent operator of dissipative operator.