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ЖУРНАЛЫ // Eurasian Mathematical Journal // Архив

Eurasian Math. J., 2020, том 11, номер 2, страницы 40–51 (Mi emj364)

Эта публикация цитируется в 1 статье

Hyperbolicity with weight of polynomials in terms of comparing their power

H. G. Ghazaryanab, V. N. Margaryana

a Department of Applied Mathematics and Mathematical Informatics, Russian - Armenian University, 123 Ovsep Emin St, 051, Yerevan, Republic of Armenia
b Institut of Mathematics the National Academy of Sciences of Armenia, 24/ 5 Marshal Baghramyan Ave, 0019 Yerevan, Republic of Armenia

Аннотация: For a given completely regular Newton polyhedron $\mathfrak{R}$, and a given vector $N\in\mathbb{R}^n$, we give conditions under which a weakly hyperbolic polynomial (with respect to the vector $N$) $P(\xi)=P(\xi_1,\dots,\xi_n)$ is $\mathfrak{R}$-hyperbolic (with respect to the vector $N$). For polynomials of two variables, the largest number $s >0$ is determined for which an $\mathfrak{R}$-hyperbolic (with respect to the vector $N$) polynomial is $s$-hyperbolic.

Ключевые слова и фразы: hyperbolic by Gärding polynomial, weak hyperbolic polynomial, hyperbolic with the weight polynomial, completely regular Newtons polyhedron.

MSC: 12E10, 35L25, 35B51, 35E20

Поступила в редакцию: 08.04.2019

Язык публикации: английский

DOI: 10.32523/2077-9879-2020-11-2-40-51



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