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Non‐self‐adjoint Bessel and Sturm–Liouville boundary value problems in limit‐circle case
Author(s) -
Allahverdiev Bilender P.
Publication year - 2014
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.3144
Subject(s) - mathematics , bessel function , hilbert space , sturm–liouville theory , mathematical analysis , dissipative operator , dissipative system , eigenvalues and eigenvectors , operator (biology) , self adjoint operator , limit (mathematics) , perturbation (astronomy) , boundary value problem , pure mathematics , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , gene
It is shown in the limit‐circle case that system of root functions of the non‐self‐adjoint maximal dissipative (accumulative) Bessel operator and its perturbation Sturm–Liouville operator form a complete system in the Hilbert space. Furthermore, asymptotic behavior of the eigenvalues of the maximal dissipative (accumulative) Bessel operators is investigated, and it is proved that system of root functions form a basis (Riesz and Bari bases) in the same Hilbert space. Copyright © 2014 John Wiley & Sons, Ltd.