Content uploaded by Yuri Borysovych Zelinskii
Author content
All content in this area was uploaded by Yuri Borysovych Zelinskii on Jan 09, 2016
Content may be subject to copyright.
On analytical conditions of generalized linear
convexity
Yu.B. Zelinskii, M.V. Tkachuk, T.M. Osipchuk
otm82@mail.ru
Institute of mathematics of NAS of Ukrain, Kyiv
In terms of nonnegativity and positivity of some special quadratic dif-
ferential forms we give, respectively, necessary and sucient conditions of
local linear convexity of domains with smooth boundary in multidimension-
al spaces under the algebra of real quaternions, the algebra of generalized
quaternions and the Cliord algebras. These conditions are natural coun-
terparts of analytical conditions of local linear convexity of domains with
smooth boundary in multidimensional complex space proposed by B. Zi-
noviev in 1971.
(1) Zinoviev B.S.
Analitic conditions and some questions of approxima-
tion of linear convex domains with smooth boundaries in the space
Cn
// Izv. vuzov, Math., 1971, No 6, P. 61- 69.
(2) Osipchuk T.M.
Analitic conditions of local linear convexity in
Hn
//
Zb. prats of the Inst. of Math. of NASU, 2006,
3
, No 3, P. 244 - 254
(in Ukrainian).
(3) Osipchuk T.M., Zelinskii Yu.B., Tkachuk M.V.
Analytical condi-
tions of locally general convexity in
Cm
p,q
// Zb. prats of the Inst. of
Math. of NASU, 2010,
7
, No 2, P. 393 - 401 (in Ukrainian).
(4) Osipchuk T.M.
Analytical conditions of local linear convexity in the
space
Hn
α,β
// Zb. prats of the Inst. of Math. of NASU, 2013,
10
,
No 45, P. 301- 305.
1