o:1730 Singular Sylvester equation and its applications Singularna Silvesterova jednačina i njene primene : doctoral dissertation en This thesis concerns singular Sylvester operator equations, that is, equations of the form AX-XB=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, Sturm-Liouville inverse problems and some operator equations from quantum mechanics. Biografija autora sa bibliografijom: str. 111-113;Bibliografija: str. 101-109. Datum odbrane: 09.02.2021. Functional analysis 37827081 91552101 8234 91552100 37827081 2021-08-24T14:04:01.053Z 45 no 46 mentor Bogdan D. 1993- Đorđević 2020 63 mentor Nebojša Č. 1983- Dinčić 2020 63 član komisije Vladimir 1953- Rakočević 2020 63 član komisije Stevan 1950- Pilipović 2020 63 član komisije Peter 1962- Šemrl 2020 63 član komisije Snežana 1965- Živković-Zlatanović 2020 63 član komisije Dijana 1981- Mosić 2020 VIII, 113 str. 6912920 http://phaidrabg.bg.ac.rs/o:1730 no yes 4 2021-08-24T14:04:01.320Z 70 Sylvester equation; operator equations; operator algebras; spectral theory of operators; closed operators; Fredholm theory; Banach algebras Silvesterova jednačina; operatorske jednačine; algebre operatora; spektralna teorija operatora; zatvoreni operatori; Fredholmova teorija; Banahove algebre 517.983.23(043.3) P140 1738 18A07 18A0701 2020