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The discreteness of the spectrum of the Schrödinger operator equation and some properties of the s ‐numbers of the inverse Schrödinger operator
Author(s) -
Hashimoglu Ilyas,
Akın Ömer,
Mamedov Khanlar R.
Publication year - 2019
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.5489
Subject(s) - mathematics , operator (biology) , spectrum (functional analysis) , mathematical analysis , inverse , laplace operator , hilbert space , schrödinger equation , displacement operator , schrödinger's cat , green's function for the three variable laplace equation , mathematical physics , inverse laplace transform , laplace transform , finite rank operator , quasinormal operator , quantum mechanics , banach space , physics , geometry , biochemistry , chemistry , repressor , transcription factor , gene
In this article, we investigate the discreteness and some other properties of the spectrum for the Schrödinger operator L defined by the formula Ly = −d 2 y d x 2+ A A + Ix 2 y + Q x y on the space L 2 ( H , [0, ∞)) , where H is a Hilbert space. For the first time, an estimate is obtained for sum of the s ‐numbers of the inverse Schrödinger operator. The obtained results were applied to the Laplace's equation in an angular region.