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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......................................................................................................................................................1691991 Mathematics Subject Classification: Primary 34Gxx, 45A05, 45Exx, 47E05.
Nguyen Van Mau. Boundary value problems and controllability of linear systems with right invertible operators. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1992. <http://eudml.org/doc/219355>.
@book{NguyenVanMau1992, abstract = {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......................................................................................................................................................1691991 Mathematics Subject Classification: Primary 34Gxx, 45A05, 45Exx, 47E05.}, author = {Nguyen Van Mau}, keywords = {differentiation operator; right inverse; Volterra operator; right invertible operator; generalized inverses; initial and boundary value problems; controllability; differential and integral operators; algebraic approach}, language = {eng}, location = {Warszawa}, publisher = {Instytut Matematyczny Polskiej Akademi Nauk}, title = {Boundary value problems and controllability of linear systems with right invertible operators}, url = {http://eudml.org/doc/219355}, year = {1992}, }
TY - BOOK AU - Nguyen Van Mau TI - Boundary value problems and controllability of linear systems with right invertible operators PY - 1992 CY - Warszawa PB - Instytut Matematyczny Polskiej Akademi Nauk AB - 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......................................................................................................................................................1691991 Mathematics Subject Classification: Primary 34Gxx, 45A05, 45Exx, 47E05. LA - eng KW - differentiation operator; right inverse; Volterra operator; right invertible operator; generalized inverses; initial and boundary value problems; controllability; differential and integral operators; algebraic approach UR - http://eudml.org/doc/219355 ER -