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Uspekhi Mat. Nauk, 1978, Volume 33, Issue 4(202), Pages 141–168 (Mi umn3462)  

This article is cited in 32 scientific papers (total in 32 papers)

Unitary operator colligations and their characteristic functions

M. S. Brodskii


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English version:
Russian Mathematical Surveys, 1978, 33:4, 159–191

Bibliographic databases:

UDC: 517.4
MSC: 47A48, 47A68, 47A70
Received: 16.04.1977

Citation: M. S. Brodskii, “Unitary operator colligations and their characteristic functions”, Uspekhi Mat. Nauk, 33:4(202) (1978), 141–168; Russian Math. Surveys, 33:4 (1978), 159–191

Citation in format AMSBIB
\Bibitem{Bro78}
\by M.~S.~Brodskii
\paper Unitary operator colligations and their characteristic functions
\jour Uspekhi Mat. Nauk
\yr 1978
\vol 33
\issue 4(202)
\pages 141--168
\mathnet{http://mi.mathnet.ru/umn3462}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=510672}
\zmath{https://zbmath.org/?q=an:0386.47003|0415.47007}
\transl
\jour Russian Math. Surveys
\yr 1978
\vol 33
\issue 4
\pages 159--191
\crossref{https://doi.org/10.1070/RM1978v033n04ABEH002495}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. P. Ginzburg, “Almost-invariant properties of analytic operator families”, Funct. Anal. Appl., 16:1 (1982), 55–56  mathnet  crossref  mathscinet  zmath  isi
    2. Yves Genin, Paul Van Dooren, Tom Kailath, Jean-Marc Delosme, Martin Morf, “On ∑-lossless transfer functions and related questions”, Linear Algebra and its Applications, 50 (1983), 251  crossref
    3. D. C. Youla, H. J. Carlin, B. S. Yarman, “Double broadband matching and the problem of reciprocal reactance 2n-port cascade decomposition”, Int J Circ Theor Appl, 12:3 (1984), 269  crossref  zmath  isi
    4. A. P. Filimonov, È. R. Tsekanovskii, “Automorphic-invariant operator colligations and the factorization of their characteristic operator functions”, Funct. Anal. Appl., 21:4 (1987), 343–344  mathnet  crossref  mathscinet  zmath  isi
    5. V. A. Zolotarev, “Model representations of commutative systems of linear operators”, Funct. Anal. Appl., 22:1 (1988), 55–57  mathnet  crossref  mathscinet  zmath  isi
    6. Louis de Branges, “Krein spaces of analytic functions”, Journal of Functional Analysis, 81:2 (1988), 219  crossref
    7. Ðo Cong Khanh, “$(\pm)$-regular factorization and the best minorant”, Funct. Anal. Appl., 25:1 (1991), 59–60  mathnet  crossref  mathscinet  zmath  isi
    8. H. Lev-Ari†, T. Kailath, “State-space approach to factorization of lossless transfer functions and structured matrices”, Linear Algebra and its Applications, 162-164 (1992), 273  crossref
    9. Joseph A Ball, Tavan T Trent, “Unitary Colligations, Reproducing Kernel Hilbert Spaces, and Nevanlinna–Pick Interpolation in Several Variables”, Journal of Functional Analysis, 157:1 (1998), 1  crossref
    10. D. Z. Arov, “Conditions for the Similarity of All Minimal Passive Scattering Systems with Given Scattering Matrix”, Funct. Anal. Appl., 34:4 (2000), 293–295  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. S.S. Boiko, V.K. Dubovoy, “Unitary Couplings, Scattering Suboperators and Regular Factorizations of Bounded Operator Valued Functions”, Math Nachr, 236:1 (2002), 47  crossref  mathscinet  zmath  isi
    12. M. M. Malamud, V. I. Mogilevskii, “Generalized Resolvents of Symmetric Operators”, Math. Notes, 73:3 (2003), 429–435  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. V. A. Zolotarev, “On isometric dilations of commutative systems of linear operators”, Zhurn. matem. fiz., anal., geom., 1:2 (2005), 192–208  mathnet  mathscinet  zmath  elib
    14. Jarmo Malinen, Olof J. Staffans, “Conservative boundary control systems”, Journal of Differential Equations, 231:1 (2006), 290  crossref
    15. V. Havu, J. Malinen, “The Cayley Transform as a Time Discretization Scheme”, Num. Functional Analysis & Optimization, 28:7 (2007), 825  crossref
    16. V. A. Zolotarev, “Scattering scheme with many parameters and translational models of commutative operator systems”, Zhurn. matem. fiz., anal., geom., 3:4 (2007), 424–447  mathnet  mathscinet  zmath  elib
    17. Tikhonov A., “On Connection Between Factorizations of Weighted Schur Functions and Invariant Subspaces”, Operator Theory, Analysis and Mathematical Physics, Operator Theory : Advances and Applications, 174, eds. Janas J., Kurasov P., Laptev A., Naboko S., Stolz G., Birkhauser Verlag Ag, 2007, 205–246  crossref  isi
    18. D. Z. Arov, N. A. Rozhenko, “To the theory of passive systems of resistance with losses of scattering channels”, J. Math. Sci. (N. Y.), 156:5 (2009), 742–760  mathnet  crossref  zmath
    19. V. A. Zolotarev, “Functional model of commutative operator systems”, Zhurn. matem. fiz., anal., geom., 4:3 (2008), 420–440  mathnet  mathscinet  zmath  elib
    20. Arlinskii Yu., Golinskii L., Tsekanovskii E., “Contractions with Rank One Defect Operators and Truncated CMV Matrices”, J. Funct. Anal., 254:1 (2008), 154–195  crossref  isi
    21. Sander Wahls, Holger Boche, Volker Pohl, “Zero-forcing precoding for frequency selective MIMO channels with criterion and causality constraint”, Signal Processing, 89:9 (2009), 1754  crossref
    22. Daniel Alpay, Andrey Melnikov, Victor Vinnikov, “Un algorithme de Schur pour les fonctions de transfert des systèmes surdéterminés invariants dans une direction”, Comptes Rendus Mathematique, 347:13-14 (2009), 729  crossref
    23. Tikhonov A., “Inverse Problem for Conservative Curved Systems”, Modern Analysis and Applications: Mark Krein Centenary Conference, Vol 1, Operator Theory Advances and Applications, 190, eds. Adamyan V., Berezansky Y., Gohberg I., Gorbachuk M., Gorbachuk V., Kochubei A., Langer H., Popov G., Birkhauser Verlag Ag, 2009, 471–490  crossref  isi
    24. Yury A. Neretin, “Multi-operator colligations and multivariate characteristic functions”, Anal.Math.Phys, 2011  crossref
    25. Yu. A. Neretin, “Sphericity and multiplication of double cosets for infinite-dimensional classical groups”, Funct. Anal. Appl., 45:3 (2011), 225–239  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    26. Boiko S.S., Dubovoy V.K., “Defect Functions of Holomorphic Contractive Operator Functions and the Scattering Suboperator Through the Internal Channels of a System. Part I”, Complex Anal. Oper. Theory, 5:1 (2011), 157–196  crossref  isi
    27. Yury Neretin, “Symmetries of Gaussian measures and operator colligations”, Journal of Functional Analysis, 2012  crossref
    28. J.A.. Ball, Mikael Kurula, O.J.. Staffans, Hans Zwart, “De Branges–Rovnyak Realizations of Operator-Valued Schur Functions on the Complex Right Half-Plane”, Complex Anal. Oper. Theory, 2014  crossref
    29. Yu. A. Neretin, “Infinite-dimensional $p$-adic groups, semigroups of double cosets, and inner functions on Bruhat–Tits buildings”, Izv. Math., 79:3 (2015), 512–553  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    30. Yu. A. Neretin, “Radial parts of Haar measures and probability distributions on the space of rational matrix-valued functions”, Izv. Math., 80:6 (2016), 1118–1130  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    31. Yu. A. Neretin, “Multiplication of conjugacy classes, colligations, and characteristic functions of matrix argument”, Funct. Anal. Appl., 51:2 (2017), 98–111  mathnet  crossref  crossref  isi  elib
    32. J. Math. Sci. (N. Y.), 240:5 (2019), 572–586  mathnet  crossref
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