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 Mat. Zametki, 1977, Volume 22, Issue 2, Pages 161–166 (Mi mz8037)

Determination of a neighborhood of the imaginary axis which is disjoint from the spectrum of a real polynomial

K. L. Olifirov

Abstract: The distance of the spectrum of $f$ from the imaginary axis is estimated for a real polynomial $f(z)=\sum_{\nu=0}^na_\nu z^\nu$ with roots in the right (or as a corollary, in the left) half plane: $f:\min\operatorname{Resp}(f)\ge-1/\operatorname{tr}(H_1H^{-1})>0$ where $H:=[a_{n+i-2j}]_{i,j=\overline{1,n}}$ and $H_1:=[ka_k]$, $k:=n+i-2j+1$, $i,j=\overline{1,n}$.

Full text: PDF file (376 kB)

English version:
Mathematical Notes, 1977, 22:2, 581–584

Bibliographic databases:

UDC: 512.3

Citation: K. L. Olifirov, “Determination of a neighborhood of the imaginary axis which is disjoint from the spectrum of a real polynomial”, Mat. Zametki, 22:2 (1977), 161–166; Math. Notes, 22:2 (1977), 581–584

Citation in format AMSBIB
\Bibitem{Oli77} \by K.~L.~Olifirov \paper Determination of a~neighborhood of the imaginary axis which is disjoint from the spectrum of a~real polynomial \jour Mat. Zametki \yr 1977 \vol 22 \issue 2 \pages 161--166 \mathnet{http://mi.mathnet.ru/mz8037} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=492192} \zmath{https://zbmath.org/?q=an:0359.30001} \transl \jour Math. Notes \yr 1977 \vol 22 \issue 2 \pages 581--584 \crossref{https://doi.org/10.1007/BF01780964}