Naslov (eng)

Singular Sylvester equation and its applications

Autor

Đorđević, Bogdan D. 1993-

Doprinosi

Dinčić, Nebojša Č. 1983-
Rakočević, Vladimir 1953-
Pilipović, Stevan 1950-
Šemrl, Peter 1962-
Živković-Zlatanović, Snežana 1965-
Mosić, Dijana 1981-

Opis (eng)

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.

Opis (eng)

Biografija autora sa bibliografijom: str. 111-113;Bibliografija: str. 101-109. Datum odbrane: 09.02.2021. Functional analysis

Jezik

engleski

Datum

2020

Licenca

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Creative Commons CC BY-NC-ND 2.0 AT - Creative Commons Autorstvo - Nekomercijalno - Bez prerada 2.0 Austria License.

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