Boundary value problems and controllability of linear systems with right invertible operators

Nguyen, Van Mau

Książka - szczegóły

Tytuł książki

Boundary value problems and controllability of linear systems with right invertible operators

Autorzy

Nguyen Van Mau

Seria

Rozprawy Matematyczne tom/nr w serii: 316 wydano: 1992

Zawartość

Pełne teksty:

http://matwbn.icm.edu.pl/ksiazki/rm/rm316/rm31601.pdf [zdalny]

Warianty tytułu

Abstrakty

EN

CONTENTS
Introduction..........................................................................................................................................................5
Preliminaries........................................................................................................................................................7
   1. Linear spaces and linear operators..............................................................................................................7
   2. Right and left invertible operators................................................................................................................8
   3. Algebraic operators....................................................................................................................................12
   4. Singular integral operators.........................................................................................................................15
I. 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................................................................................................................................32
II. 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...................................................................................62
III. 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......................................................................................133
IV. 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...........................161
References......................................................................................................................................................169

Słowa kluczowe

Tematy

Kategoryzacja MSC:

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 316

Liczba stron

171

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CCCXVI

Daty

wydano

1992

otrzymano

1990-10-09

Twórcy

autor

Nguyen Van Mau

Faculty of Mathematics, University of Hanoi, Hanoi, Vietnam

Bibliografia

[1] G. R. Allan, On one-side inverses in Banach algebras of holomorphic vector valued functions, J. London Math. Soc. 42 (1967), 460-470.
[2] P. M. Anselone and M. Z. Nashed, Perturbations of outer inverses, in: Approximation Theory III, Academic Press, New York 1980, 163-169.
[3] R. Arens, Dense inverses limit rings, Michigan Math. J. 5 (1958), 169-182.
[4] A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, Wiley-Interscience, New York 1974.
[5] L. Berg, Randwertsprobleme in der Operatorenrechnung, Wiss. Z. Univ. Rostock 23 (1974), 621-624.
[6] L. Berg, Rechtinverse Operatoren und Randprojektionen, Math. Nachr. 129 (1986), 21-29.
[7] Z. Binderman, Initial operators for generalized invertible operators, Comment. Math., to appear.
[8] T. L. Boullion and P. L. Odell, Generalized Inverse Matrices, Wiley-Interscience, New York 1974.
[9] S. L. Campbell and C. D. Meyer, Generalized Inverses of Linear Transformations, Pitman, London 1979.
[10] S. R. Caradus, Generalized Inverses and Operator Theory, Queen's Papers in Pure and Appl. Math. 50, Queen's Univ., Kingston, Ont., 1978.
[11] I. H. Dimovski, Duhamel-type representations of the solutions of non-local boundary value problems, in: Proc. Second Conf. Differential Equations and Applications, Rousse 1981, Techn. Univ. Rousse, 1982, 240-247.
[12] I. H. Dimovski and R. I. Petrova, Generalized solutions of non-local problems, in: Proc. 17-th Spring Conf. Bulgar. Math. Union, Mathematics and Math. Education, April 1988, Bulgar. Acad. Sci., Sofia 1988, 161-165.
[13] M. M. Dzhrbashyan and B. A. Saakyan, Classes of formulas and expansions of Taylor-Maclaurin type associated with differential operators of fractional order, Izv. Akad. Nauk SSSR 39 (1975), 65-122 (in Russian).
[14] F. D. Gakhov, Boundary Value Problems, Oxford 1966 (3rd Russian complemented and corrected edition, Moscow 1977).
[15] I. S. Gokhberg and N. Y. Krupnik, Introduction to the Theory of One-Dimensional Singular Integral Operators, Kishinev 1973 (in Russian).
[16] L. Jodar, Algebraic methods for solving boundary value problems, Stochastica 10 (1986), 259-270.
[17] Ch. Kahane, On operators commuting with differentiation, Amer. Math. Monthly 76 (1969), 171-173.
[18] W. Z. Karwowski, Nonlinear boundary value problems with right invertible operators, Ph. D. diss., Institute of Mathematics, Technical University of Warsaw, Warszawa 1988 (in Polish).
[19] W. Z. Karwowski and D. Przeworska-Rolewicz, Green operators for linear boundary value problems with a right invertible operator $D^N$, Math. Nachr. 152 (1991), to appear.
[20] W. Z. Karwowski and D. Przeworska-Rolewicz, Linear boundary value problems for polynomials in right invertible operators, Demonstratio Math., to appear.
[21] H. Kornacki, Linear equations with right invertible operators and their right inverses in spaces of Dirichlet series, Ph. D. diss., Institute of Mathematics, Technical University of Warsaw, Warszawa 1988 (in Polish).
[22] A. Lausch and D. Przeworska-Rolewicz, Pseudocategories, paraalgebras and linear operators, Math. Nachr. 138 (1988), 67-82.
[23] S. G. Mikhlin and S. Prössdorf, Singular Integral Operators, Berlin 1986.
[24] D. Milman, The abstract linear boundary value problem ( a nongroup approach), Integral Equations Operator Theory 9 (1986), 11-30.
[25] M. Z. Nashed (ed.), Generalized Inverses and Applications, Academic Press, New York 1976.
[26] M. Z. Nashed, Inner, outer and generalized inverses in Banach and Hilbert spaces, Numer. Funct. Anal. Optim. 9 (1987), 261-325.
[27] Nguyen Dinh Quyet, Controllability and observability of linear systems described by the right invertible operators in linear spaces, preprint No. 113, Institute of Mathematics, Polish Acad. Sci., Warszawa 1977.
[28] Nguyen Dinh Quyet, On linear systems described by right invertible operators acting in a linear space, Control and Cybernetics, 7 (1978), 33-45.
[29] Nguyen Dinh Quyet, On the stability and observability of (D-R)-systems in Banach spaces, Demonstratio Math. 12 (1979), 203-209.
[30] Nguyen Van Mau, Remarks on initial value problems for equations with right invertible operators, preprint No. 451, Institute of Mathematics, Polish Acad. Sci., Warszawa 1989.
[31] Nguyen Van Mau, Generalized Algebraic Elements and Linear Singular Integral Equations with Transformed Argument, Wydawnictwa Politechniki Warszawskiej, Warszawa 1989.
[32] Nguyen Van Mau, Boundary and mixed boundary value problems for equations with right invertible operators, preprint No. 465, Institute of Mathematics, Polish Acad. Sci., Warszawa 1989.
[33] Nguyen Van Mau, On solutions of a system of singular integral equations with analytic kernals and reflection, Ann. Polon. Math. 52 (1990), 103-108 (in Russian).
[34] Nguyen Van Mau, On ill-determined equations in right invertible operator of order one in non-commutative case, Math. Nachr. 147 (1990), 81-91.
[35] Nguyen Van Mau, Controllability of general linear systems with right invertible operators, preprint No. 472, Institute of Mathematics, Polish Acad. Sci., Warszawa 1990.
[36] Nguyen Van Mau, Interpolation problems induced by right and left invertible operators and its applications to singular integral equations, Demonstratio Math. 23 (1990), 191-212.
[37] Nguyen Van Mau, Characterization of Volterra right inverses, Opuscula Math. 6 (1990), 21-37.
[38] Nguyen Van Mau, Conditions for polynomials in right inverses with stationary and algebraic coefficients to be Volterra, Comment. Math. 30 (1991), 175-185.
[39] Nguyen Van Mau, Properties of generalized almost inverses, Demonstratio Math., to appear.
[40] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc. 51 (1955), 406-413.
[41] A. Pogorzelec, Initial value problems with ill-determined linear systems with right invertible operators, Demonstratio Math. 16 (1983), 407-420.
[42] A. Pogorzelec, Solvability of linear systems of the first order with right invertible operators, ibid. 18 (1985), 1039-1063.
[43] A. Pogorzelec, Solvability and controllability of ill-determined systems with right invertible operators, Ph. D. Diss., Institute of Mathematics, Technical University of Warsaw, Warszawa 1983.
[44] D. Przeworska-Rolewicz, Equations with Transformed Argument. An Algebraic Approach, Elsevier and PWN, Amsterdam-Warszawa 1973.
[45] D. Przeworska-Rolewicz, Shifts and Periodicity for Right Invertible Operators, Res. Notes in Math. 43, Pitman, Boston 1980.
[46] D. Przeworska-Rolewicz, Algebraic Analysis, PWN and Reidel, Warszawa-Dordrecht 1988.
[47] D. Przeworska-Rolewicz, Linear boundary value problems for right invertible operators, preprint No. 413, Institute of Mathematics, Polish Acad. Sci., Warszawa 1988.
[48] D. Przeworska-Rolewicz, Property (c) and interpolation formulae induced by right invertible operators, Demonstratio Math. 21 (1988), 1023-1044.
[49] D. Przeworska-Rolewicz, Spaces of D-paraanalytic elements, Dissertationes Math. 302 (1990).
[50] D. Przeworska-Rolewicz and S. Rolewicz, Equations in Linear Spaces, Monografie Mat. 47, PWN, Warszawa 1968.
[51] D. Przeworska-Rolewicz and S. Rolewicz, The only continuous Volterra right inverses in $C_c[0,1]$ for the operator d/dt are $∫_a^t$, Colloq. Math. 51 (1985), 279-283.
[52] D. Przeworska-Rolewicz and S. Rolewicz, On the spectrum of right inverses, Demonstratio Math. 23 (1990), to appear.
[53] D. Przeworska-Rolewicz and H. von Trotha, Right inverses in D-R algebras with unit, J. Integral Equations 3 (1981), 245-259.
[54] S. Rolewicz, Functional Analysis and Control Theory, PWN and Reidel, Warszawa-Dordrecht 1987.
[55] F. O. Speck, Least squares approximate and least norm solutions of paired singular equations, Math. Nachr. 130 (1987), 47-68.
[56] B. Shekhtman, On some problems of M. Z. Nashed on outer inverses, Linear Algebra Appl. 76 (1986), 149-152.
[57] M. Tasche, Abstrakte lineare Differentialgleichungen mit stationären Operatoren, Math. Nachr. 78 (1977), 21-36.
[58] M. Tasche, Funktionanalytische Methoden in der Operatorenrechnung, Nova Acta Leopoldina 49, Halle 1978.
[59] M. Tasche, A unified approach to interpolation methods, J. Integral Equations 4 (1982), 55-75.
[60] H. von Trotha, Structure properties of D-R vector spaces, Dissertationes Math. 184 (1981).
[61] H. von Trotha, Contractivity in certain D-R spaces, Math. Nachr. 101 (1981), 207-213.

Języki publikacji

EN

Uwagi

1991 Mathematics Subject Classification: Primary 34Gxx, 45A05, 45Exx, 47E05.

Identyfikator YADDA

bwmeta1.element.zamlynska-a67f0819-256c-42f3-8fb9-81554e4f372a

Identyfikatory

ISBN

83-85116-27-3

ISSN

0012-3862

Kolekcja

DML-PL

Zawartość książki

rozwiń roczniki

Książka - szczegóły

Boundary value problems and controllability of linear systems with right invertible operators

Autorzy

Seria

Zawartość

Warianty tytułu

Abstrakty

Słowa kluczowe

Tematy

Wydawca

Miejsce publikacji

Copyright

Seria

Liczba stron

Liczba rozdzia³ów

Opis fizyczny

Daty

Twórcy

Bibliografia

Języki publikacji

Uwagi

Identyfikator YADDA

Identyfikatory

Kolekcja