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Sbornik: Mathematics, 2002, Volume 193, Issue 4, Pages 531–557
DOI: https://doi.org/10.1070/SM2002v193n04ABEH000644 (Mi sm644) 		 
Conditions for the non-negativity of integral quadratic forms with constant coefficients on a half-axis

A. A. Milyutin

N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences
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DOI: https://doi.org/10.1070/SM2002v193n04ABEH000644
Abstract: An integral quadratic functional with constant coefficients on a half-axis is considered. A necessary and sufficient condition for its non-negativity at all square integrable pairs of functions related by a linear ODE is proposed, which is based on the Hamilton–Jacobi inequality. A connection between this condition and the well-known frequency criterion is established.
Received: 19.09.2001
Russian version:
Matematicheskii Sbornik, 2002, Volume 193, Number 4, Pages 61–86
DOI: https://doi.org/10.4213/sm644
Bibliographic databases:
UDC: 517.97
MSC: Primary 49N10; Secondary 49L99
Language: English
Original paper language: Russian
Citation: A. A. Milyutin, “Conditions for the non-negativity of integral quadratic forms with constant coefficients on a half-axis”, Sb. Math., 193:4 (2002), 531–557
Citation in format AMSBIB
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\by A.~A.~Milyutin
\paper Conditions for the~non-negativity of integral quadratic forms with constant
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\jour Sb. Math.
\yr 2002
\vol 193
\issue 4
\pages 531--557
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    Russian version PDF:212
    English version PDF:13
    References:56
    First page:1
     
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