Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (1996) no. 1, pp. 102-117
Citer cet article
V. N. Kokarev. On complete convex solutions of the equation $\operatorname{spur}_m(z_{ij})=1$. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 3 (1996) no. 1, pp. 102-117. http://geodesic.mathdoc.fr/item/JMAG_1996_3_1_a8/
@article{JMAG_1996_3_1_a8,
author = {V. N. Kokarev},
title = {On complete convex solutions of the equation $\operatorname{spur}_m(z_{ij})=1$},
journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
pages = {102--117},
year = {1996},
volume = {3},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/JMAG_1996_3_1_a8/}
}
TY - JOUR
AU - V. N. Kokarev
TI - On complete convex solutions of the equation $\operatorname{spur}_m(z_{ij})=1$
JO - Žurnal matematičeskoj fiziki, analiza, geometrii
PY - 1996
SP - 102
EP - 117
VL - 3
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UR - http://geodesic.mathdoc.fr/item/JMAG_1996_3_1_a8/
LA - ru
ID - JMAG_1996_3_1_a8
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%D 1996
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%G ru
%F JMAG_1996_3_1_a8
Let designation $\operatorname{spur}_m(z_{ij})=1$ stand for the sum of all principal $m$-order minors of matrix $(z_{ij})$, consisting of second derivatives of the function $z(x^1,\dots,x^n)$. Any complete convex class $C^{2\alpha}$ solution of the equation $\operatorname{spur}_m(z_{ij})=1$, ($2\le m), will be a quadratic polynomial if the matrix $(z_{ij})$ eigenvalues are sufficiently close to each other.
