Geodesic
Determination of a~neighborhood of the imaginary axis which is disjoint from the spectrum of a~real polynomial
Matematičeskie zametki, Tome 22 (1977) no. 2, pp. 161-166

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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 $H_1:=[ka_k]$, $k:=n+i-2j+1$, $i,j=\overline{1,n}$. 
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     author = {K. L. Olifirov},
     title = {Determination of a~neighborhood of the imaginary axis which is disjoint from the spectrum of a~real polynomial},
     journal = {Matemati\v{c}eskie zametki},
     pages = {161--166},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a0/}
}
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K. L. Olifirov. Determination of a~neighborhood of the imaginary axis which is disjoint from the spectrum of a~real polynomial. Matematičeskie zametki, Tome 22 (1977) no. 2, pp. 161-166. http://geodesic.mathdoc.fr/item/MZM_1977_22_2_a0/