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Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 5, Pages 1108–1131 (Mi izv2354)  

This article is cited in 12 scientific papers (total in 12 papers)

On the complete $n$-tuple of roots of the operator equation cirresponding to a polynomial operator bundle

A. S. Markus, I. V. Mereutsa

Abstract: The paper treats the relationship between spectral properties of an $n$th degree polynomial operator bundle and spectral properties of roots of the corresponding operator equation. Basic to this investigation is the concept, introduced in this paper, of Vandermonde operator.

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English version:
Mathematics of the USSR-Izvestiya, 1973, 7:5, 1105–1128

Bibliographic databases:

UDC: 517.9
MSC: Primary 47A10; Secondary 47A50
Received: 26.09.1972

Citation: A. S. Markus, I. V. Mereutsa, “On the complete $n$-tuple of roots of the operator equation cirresponding to a polynomial operator bundle”, Izv. Akad. Nauk SSSR Ser. Mat., 37:5 (1973), 1108–1131; Math. USSR-Izv., 7:5 (1973), 1105–1128

Citation in format AMSBIB
\by A.~S.~Markus, I.~V.~Mereutsa
\paper On the complete $n$-tuple of roots of the operator equation cirresponding to a~polynomial operator bundle
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 5
\pages 1108--1131
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 5
\pages 1105--1128

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    This publication is cited in the following articles:
    1. V. I. Kabak, A. S. Markus, “O razlozhenii polinomialnogo puchka na lineinye mnozhiteli”, UMN, 30:4(184) (1975), 245–246  mathnet  mathscinet  zmath
    2. I Gohberg, M.A Kaashoek, L Rodman, “Spectral analysis of families of operator polynomials and a generalized Vandermonde matrix II: The infinite dimensional case”, Journal of Functional Analysis, 30:3 (1978), 358  crossref
    3. LEANG S. SHIEH, YIH T. TSAY, NORMAN P. COLEMAN, “Algorithms for solvents and spectral factors of matrix polynomials”, International Journal of Systems Science, 12:11 (1981), 1303  crossref
    4. G. V. Radzievskii, “The problem of the completeness of root vectors in the spectral theory of operator-valued functions”, Russian Math. Surveys, 37:2 (1982), 91–164  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. Yih T. Tsay, Leang S. Shieh, R.E. Yates, S. Barnett, “Block partial fraction expansion of a rational matrix”, Linear and Multilinear Algebra, 11:3 (1982), 225  crossref
    6. Yih T. Tsay, Leang S. Shieh, “Block decompositions and block modal controls of multivariable control systems”, Automatica, 19:1 (1983), 29  crossref
    7. M. S. Eremin, “On polynomial operator equations with integro-differential right-hand side”, Russian Math. Surveys, 40:1 (1985), 219–220  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. N. Chondros, J. Maroulas, “Decomposition of a rational matrix into partial fractions”, Linear and Multilinear Algebra, 18:3 (1985), 225  crossref
    9. Lucas Jódar, “Algebraic and differential operator equations”, Linear Algebra and its Applications, 102 (1988), 35  crossref
    10. H. ZABOT, K. HARICHE, “On solvents-based model reduction of MIMO systems”, International Journal of Systems Science, 28:5 (1997), 499  crossref
    11. B. Z. Shavarovskii, “Finding a complete set of solutions or proving unsolvability for certain classes of matrix polynomial equations with commuting coefficients”, Comput. Math. Math. Phys., 47:12 (2007), 1902–1911  mathnet  crossref  mathscinet  elib
    12. A. G. Baskakov, T. K. Katsaran, T. I. Smagina, “Linear differential second-order equations in Banach space and splitting of operators”, Russian Math. (Iz. VUZ), 61:10 (2017), 32–43  mathnet  crossref  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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