Title
Singular Sylvester equation and its applications
Creator
Đorđević, Bogdan D. 1993
Copyright date
2020
Object Links
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AutorstvoNekomercijalnoBez prerade 3.0 Srbija (CC BYNCND 3.0)
License description
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Language
English
CobissID
Theses Type
Doktorska disertacija
description
Datum odbrane: 09.02.2021.
Other responsibilities
mentor
Dinčić, Nebojša Č. 1983
član komisije
Rakočević, Vladimir 1953
član komisije
Pilipović, Stevan 1950
član komisije
Šemrl, Peter 1962
član komisije
ŽivkovićZlatanović, Snežana 1965
član komisije
Mosić, Dijana 1981
Academic Expertise
Prirodnomatematičke nauke
Academic Title

University
Univerzitet u Nišu
Faculty
Prirodnomatematički fakultet
Group
Odsek za matematiku i informatiku
Alternative title
Singularna Silvesterova jednačina i njene primene
Publisher
[B. D. Đorđević]
Format
VIII, 113 str.
description
Biografija autora sa bibliografijom: str. 111113;
Bibliografija: str. 101109.
description
Functional analysis
Abstract (en)
This thesis concerns singular Sylvester operator equations, that is, equations of the form AXXB=C, under the premise that they are either unsolvable or have infinitely many solutions. The equation is studied in different cases, first in the matrix case, then in the case when A, B and C are bounded linear operators on Banach spaces, and finally in the case when A and B are closed linear operators defined on Banach or Hilbert spaces. In each of these cases, solvability conditions are derived and then, under those conditions, the initial equation is solved. Exact solutions are obtained in their closed forms, and their classification is conducted. It is shown that all solutions are obtained in the manner illustrated in this thesis. Special attention is dedicated to approximation schemes of the solutions. Obtained results are illustrated on some contemporary problems from operator theory, among which are spectral problems of bounded and unbounded linear operators, SturmLiouville inverse problems and some operator equations from quantum mechanics.
Authors Key words
Sylvester equation; operator equations; operator algebras; spectral theory of operators; closed operators; Fredholm theory; Banach algebras
Authors Key words
Silvesterova jednačina; operatorske jednačine; algebre operatora; spektralna teorija operatora; zatvoreni operatori; Fredholmova teorija; Banahove algebre
Classification
517.983.23(043.3)
Subject
P140
Type
Tekst
Abstract (en)
This thesis concerns singular Sylvester operator equations, that is, equations of the form AXXB=C, under the premise that they are either unsolvable or have infinitely many solutions. The equation is studied in different cases, first in the matrix case, then in the case when A, B and C are bounded linear operators on Banach spaces, and finally in the case when A and B are closed linear operators defined on Banach or Hilbert spaces. In each of these cases, solvability conditions are derived and then, under those conditions, the initial equation is solved. Exact solutions are obtained in their closed forms, and their classification is conducted. It is shown that all solutions are obtained in the manner illustrated in this thesis. Special attention is dedicated to approximation schemes of the solutions. Obtained results are illustrated on some contemporary problems from operator theory, among which are spectral problems of bounded and unbounded linear operators, SturmLiouville inverse problems and some operator equations from quantum mechanics.
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