CONTENTSIntroduction..........................................................................................................................................................5Preliminaries........................................................................................................................................................7 1. Linear spaces and linear operators..............................................................................................................7 2. Right and left invertible operators................................................................................................................8 3. Algebraic operators....................................................................................................................................12 4. Singular integral operators.........................................................................................................................15I. Characterizations of right inverses and interpolation problems.......................................................................16 5. Operations on Volterra right inverses.........................................................................................................16 6. Characterization of polynomials in right inverses with algebraic operator coefficients................................18 7. Algebraic exponentials................................................................................................................................23 8. Property (c).................................................................................................................................................28 9. Interpolation problems................................................................................................................................32II. Generalized almost invertible operators.........................................................................................................45 10. Properties of generalized almost invertible operators...............................................................................45 11. Equations with generalized almost invertible operators.............................................................................54 12. Generalized almost invertibility of paired operators...................................................................................62III. General equations with right invertible operators..........................................................................................68 13. Pre-resolving operators............................................................................................................................68 14. Initial value problems................................................................................................................................80 15. Boundary value problems.........................................................................................................................91 16. First mixed boundary value problems.....................................................................................................102 17. Second mixed boundary value problems................................................................................................116 18. First order equations in the noncommutative case.................................................................................127 19. Remarks on general boundary value problems......................................................................................133IV. Controllability of linear systems..................................................................................................................151 20. Controllability of first order linear systems with right invertible operators................................................141 21. Controllability of general systems with right invertible operators.............................................................151 22. Controllability of linear systems described by generalized almost invertible operators...........................161References......................................................................................................................................................169
1991 Mathematics Subject Classification: Primary 34Gxx, 45A05, 45Exx, 47E05.
@book{bwmeta1.element.zamlynska-a67f0819-256c-42f3-8fb9-81554e4f372a,
author = {Nguyen Van Mau},
title = {Boundary value problems and controllability of linear systems with right invertible operators},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1992},
zbl = {0749.34034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-a67f0819-256c-42f3-8fb9-81554e4f372a}
}
Nguyen Van Mau. Boundary value problems and controllability of linear systems with right invertible operators. GDML_Books (1992), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-a67f0819-256c-42f3-8fb9-81554e4f372a/