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The one‐dimensional Schrödinger operator on bounded time scales
Author(s) -
Tuna Hüseyin,
Özek Mehmet Afşin
Publication year - 2016
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.3966
Subject(s) - bounded function , mathematics , dissipative system , dissipative operator , operator (biology) , schrödinger's cat , bounded operator , completeness (order theory) , boundary (topology) , mathematical analysis , boundary value problem , pure mathematics , quantum mechanics , physics , biochemistry , chemistry , repressor , transcription factor , gene
In this paper, we consider the one‐dimensional Schrödinger operator on bounded time scales. We construct a space of boundary values of the minimal operator and describe all maximal dissipative, maximal accretive, self‐adjoint, and other extensions of the dissipative Schrödinger operators in terms of boundary conditions. In particular, using Lidskii's theorem, we prove a theorem on completeness of the system of root vectors of the dissipative Schrödinger operators on bounded time scales. Copyright © 2016 John Wiley & Sons, Ltd.