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Sbornik: Mathematics, 2002, Volume 193, Issue 6, Pages 791–810
DOI: https://doi.org/10.1070/SM2002v193n06ABEH000657 (Mi sm657) 		 
This article is cited in 26 scientific papers (total in 26 papers)

Tests for the similarity of all minimal passive realizations of a fixed transfer function (scattering or resistance matrix)

D. Z. Arov, M. A. Nudelman

South Ukrainian State K. D. Ushynsky Pedagogical University
English version PDF (246 kB) Citations (26)
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DOI: https://doi.org/10.1070/SM2002v193n06ABEH000657
Abstract: Necessary and sufficient conditions for the transfer function of a passive linear stationary scattering (or resistance) system are found ensuring that minimal systems in this class are determined by their transfer functions up to similarity. The criteria are stated in terms of a Hankel operator the symbol of which is a contractive operator-valued function defined by the transfer function and having the meaning of the inner scattering suboperator of a simple conservative scattering (respectively, resistance) system with the transfer function in question. A connection between the similarity criterion and the corona theorem and its matrix generalizations is revealed.
Received: 03.05.2001
Russian version:
Matematicheskii Sbornik, 2002, Volume 193, Number 6, Pages 3–24
DOI: https://doi.org/10.4213/sm657
Bibliographic databases:
UDC: 517.9
MSC: Primary 47A48, 93B20; Secondary 93B28
Language: English
Original paper language: Russian
Citation: D. Z. Arov, M. A. Nudelman, “Tests for the similarity of all minimal passive realizations of a fixed transfer function (scattering or resistance matrix)”, Mat. Sb., 193:6 (2002), 3–24; Sb. Math., 193:6 (2002), 791–810
Citation in format AMSBIB
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    • This publication is cited in the following 26 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    English version PDF:8
    References:51
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