Lomadze, Vakhtang When are linear differentiation-invariant spaces differential? (English) Zbl 1136.93002 Linear Algebra Appl. 424, No. 2-3, 540-554 (2007). Summary: It is shown that a linear differentiation-invariant subspace of a \(C^{\infty }\)-trajectory space is differential (i.e., can be represented as the kernel of a linear constant-coefficient differential operator) if and only if its McMillan degree is finite. Cited in 16 Documents MSC: 93A30 Mathematical modelling of systems (MSC2010) Keywords:linear system; transfer function; convolution function; zero initial condition PDFBibTeX XMLCite \textit{V. Lomadze}, Linear Algebra Appl. 424, No. 2--3, 540--554 (2007; Zbl 1136.93002) Full Text: DOI References: [1] Atiyah, M.; Macdonald, I. G., Introduction to Commutative Algebra (1969), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0175.03601 [2] Fuhrmann, P. A., Algebraic system theory: an analyst’s point of view, J. Franklin Inst., 301, 521-540 (1976) · Zbl 0332.93001 [3] Hörmander, L., Linear Partial Differential Operators (1976), Springer: Springer New York · Zbl 0321.35001 [4] Lomadze, V., Application of vector bundles to factorization of rational matrices, Linear Algebra Appl., 288, 249-258 (1999) · Zbl 1057.14501 [5] Mikusinski, J., Operational Calculus (1959), Pergamon Press: Pergamon Press London · Zbl 0088.33002 [6] Schumacher, J. M., Transformations of linear systems under external equivalence, Linear Algebra Appl., 102, 1-34 (1988) · Zbl 0668.93019 [7] Polderman, J. W.; Willems, J. C., Introduction to Mathematical Systems Theory (1998), Springer: Springer New York [8] Willems, J. C., Paradigms and puzzles in the theory of dynamical systems, IEEE Trans. Automat. Control, 36, 259-294 (1991) · Zbl 0737.93004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.