Multidimensional constant linear systems

Ulrich Oberst1
1Institut für Mathematik der Universität Innsbruck, Innsbruck, Austria

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Tài liệu tham khảo

Baratchart L., On discrete n-dimensional linear constant systems, in [BL], 3?8

Berg L., Introduction to the operational calculus, North-Holland 1967

Bisiacco M., E. Fornasini, G. Marchesini, Dynamic regulation of 2d-systems: A state space approach, Linear Algebra and its Applications 122?124 (1989), 195?218

Björk J.-E., Rings of Differential Operators, North-Holland 1979

Byrnes C.I., A. Lindquist (Eds.), Frequency Domain and State Space Methods for Linear Systems, North-Holland 1986

Byrnes C.I., C.F. Martin (Eds.), Geometrical Methods for the Theory of Linear Systems, D.Reidel 1980

Borel A. et al., Algebraic D-modules, Academic Press 1989

Bose N. K. (Editor), Multidimensional systems: Theory and applications, IEEE Press 1979, New York

Bose N. K. (Editor), Multidimensional systems theory, D. Reidel Publishing Company 1985

Bourbaki N., Commutative algebra, Hermann, Paris 1972

Bourbaki N., Algèbre Ch. 10 (Algèbre homologique), Masson, Paris 1980

Bourbaki N., Theorie des Ensembles I, Hermann 1956

Buchberger B., Gröbner bases: An algorithmic method in polynomial ideal theory, in [BOS2], 184?232

Blomberg H., R. Ylinen, Algebraic theory for multivariable linear systems, Academic Press 1983

Chen W. K., Applied graph theory. Graphs and electrical networks, North-Holland 1976

Conte G., A.M.Perdon, T.Kaczorek, A geometric approach to singular 2D linear systems, Proc. IFAC workshop Prague 1988

Ehrenpreis L., Fourier analysis in several complex variables, Wiley Interscience Publishers 1970

Fornasini E., G. Marchesini, State-space realization theory of two-dimensional filters, IEEE Trans. Aut. Cont. 21 (1976), 484?492

Fornasini E., Doubly indexed dynamical systems: State-space models and structural properties, Math. Systems Theory 12 (1978), 59?72

Fornasini E., Structure and Properties of Two-Dimensional Systems, in [TZ], 37?88

Furukawa A., T.Sasaki, H.Kobayashi, Gröbner basis of a module over K[x1,?,xn] and polynomial solutions of a system of linear equations, Proc. Symsac 1986 (Waterloo), 1986

Fuchs L., Teilweise geordnete algebraische Strukturen, Vandenhoek und Ruprecht 1966

Gabriel P., Etude infinitésimale des schémas en groupes, in Sch?mas en Groupes I, Lecture Notes in Mathematics 151 (1970), 476?562, Springer Verlag

Grauert H., R. Remmert, Analytische Stellenalgebren, Springer 1971

Grauert H., R. Remmert, Coherent analytic sheaves, Springer 1984

Grauert H., R. Remmert, Theorie der Steinschen Räume, Springer 1977

Gregor J., Convolutional solutions of partial difference equations, preprint 1988, to appear in MCSS

Hauger G., Injektive Moduln über Ringen linearer Differentialoperatoren, Monatshefte Math. 86 (1978), 189?201

Hironaka H., Resolution of singularities of an algebraic variety over a field of characteristic zero I, II, Ann.Math. 79 (1964), 109?326

Hörmander L., The analysis of linear partial differential operators I, Springer 1983

Hörmander L., Complex analysis in several variables, North-Holland 1973

Jacobson N., Structure of rings, American Mathematical Society Colloquium Publications 37, Providence 1968

Kailath T., Linear systems, Prentice-Hall 1980

Kamen E.W., An operator theory of linear functional differential equations, J. Diff. Equations 27 (1978), 274?297

Kashiwara M., Systems of microdifferential equations, Birkhäuser 1983

Kashiwara M., T. Kawai, T. Kimura, Foundations of algebraic analysis, Princeton University Press 1986

Köthe G., Topologische lineare Räume I, Springer 1960

Kuo B.C., Automatic Control Systems, Prentice-Hall 1987

Lejeune-Jalabert M., Effectivité de calcul polynomiaux, Cours de DEA 1984/85, Université de Grenoble

Lelong P., Fonctionelles analytiques et fonctions entières (n variables), Les Presses de l'Université de Montreal 1968

Lim J.S., A.V. Oppenheim (Editors), Advanced topics in signal processing, Prentice Hall 1988

Macaulay M.S., The algebraic theory of modular systems, Cambridge 1916, reprint by Stechert-Hafner 1964

Macaulay M.S., Some properties of enumeration in the theory of modular systems, Proc.London Math.Soc. 26(1927), 531?555

Malgrange B., Systèmes différentiels à coefficients constants, in Séminaire Bourbaki Vol. 1962/1963, 246.01?246.11

Matlis E., Injective modules over noetherian rings, Pac. J. Math. 8 (1958), 511?528

Matsumura M., Commutative ring theory, Cambridge University Press 1986

Morf M., B. Levy, S.-Y. Kung, New results on 2-d systems theory I: 2-d polynomial matrices, factorizations and coprimeness, in [BOS1], p. 54?65

Mumford D., Introduction to algebraic geometry, Lecture Notes, Harvard University.

Oberst U., Duality theory for Grothendieck categories and linearly compact rings, J. Algebra 15 (1970), 473?542

Oberst U., Multidimensional constant linear systems I, II, III, Innsbruck July 1988?January 1989, Preprints

Palamodov V.P., Linear differential operators with constant coefficients, Springer 1970

Pauer F., Gröbner Basen und ihre Anwendungen, to appear in Überblicke Mathematik, Vieweg 1990

Przeworska-Rolewicz D., Algebraic Analysis, D. Reidel 1988

Rocha P., Structure and Representation of 2-D Systems, Thesis, Groningen, February 1990

Roesser R. P., A discrete state-space model for linear image processing, IEEE Trans. Aut. Cont. 20 (1975), 1?10

Roos J.E., Locally noetherian categories and generalized strictly linearly compact rings. Applications, in Lecture Notes in Mathematics 92 (1969), 197?277, Springer

Rosenbrock H., State-space and multivariable theory, Nelson 1970

Rouchaleau Y., E.D. Sontag, On the existence of minimal realizations of linear dynamical systems over noetherian integral domains, J. Comp. Syst. Sci. 18 (1979), 65?75

Rocha P., J.C. Willems, State for 2-d systems, Lin. Alg. Appl. 122?124 (1989), 1003?1038

Rouchaleau Y., B.F. Wyman, R.E. Kalman, Algebraic structure of linear dynamical systems III. Realization theory over a commutative ring, Proc. Nat. Acad. Sci. (USA) 69 (1972), 3404?3406

Schwartz L., Théorie des distributions, Tome I, II, Hermann, Paris, 1957, 1959.

Treves F., Basic linear partial differential equations, Academic Press 1975

Tzafestas S.G. (Editor), Multidimensional systems. Techniques and applications, M. Dekker 1986

Willems J.C., From time-series to linear systems. Part I: Finite dimensional linear time-invariant systems, Automatica 22 (1986), 561?580

Willems J.C., The analysis of feedback systems, MIT Press 1971

Winkler F., A recursive method for computing a Gröbner basis of a module in K[X]r, AAECC-5

Wolowich W.A., Linear Multivariable Systems, Springer 1974

Youla D.G., G. Gnavi, Notes on n-dimensional system theory, IEEE Trans.Circ.Syst. 26(1979), 105?111