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Non‐self‐adjoint singular second‐order dynamic operators on time scale
Author(s) -
Allahverdiev Bilender P.
Publication year - 2018
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.5338
Subject(s) - mathematics , dissipative operator , dissipative system , dilation (metric space) , operator (biology) , hilbert space , completeness (order theory) , mathematical analysis , pure mathematics , quasinormal operator , self adjoint operator , finite rank operator , banach space , combinatorics , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , gene
In this study, maximal dissipative second‐order dynamic operators on semi‐infinite time scale are studied in the Hilbert spaceL r 2 ( T + ) , that the extensions of a minimal symmetric operator in limit‐point case. We construct a self‐adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax‐Phillips. Moreover, we construct a functional model of the dissipative operator and identify its characteristic function in terms of the Weyl‐Titchmarsh function of a self‐adjoint second‐order dynamic operator. Finally, we prove the theorems on completeness of the system of root functions of the dissipative and accumulative dynamic operators.