Gaddum’s test for symmetric cones

2020 ◽  
Author(s):  
Michael Orlitzky
Keyword(s):  
Symmetric Cones

Z-transformations on proper and symmetric cones

2007 ◽  
Vol 117 (1-2) ◽  
pp. 195-221 ◽  
Author(s):  
M. Seetharama Gowda ◽  
Jiyuan Tao
Keyword(s):  
Symmetric Cones

Heat Kernels of Lorentz Cones

1999 ◽  
Vol 42 (2) ◽  
pp. 169-173 ◽  
Author(s):  
Hongming Ding
Keyword(s):  
Heat Kernel ◽  
Explicit Formula ◽  
Lower Bounds ◽  
Heat Kernels ◽  
Upper And Lower Bounds ◽  
Symmetric Cones ◽  
Lorentz Cone

AbstractWe obtain an explicit formula for heat kernels of Lorentz cones, a family of classical symmetric cones. By this formula, the heat kernel of a Lorentz cone is expressed by a function of time t and two eigenvalues of an element in the cone. We obtain also upper and lower bounds for the heat kernels of Lorentz cones.

scholarly journals The decompositions with respect to two core non-symmetric cones

2019 ◽  
Vol 76 (1) ◽  
pp. 155-188
Author(s):  
Yue Lu ◽  
Ching-Yu Yang ◽  
Jein-Shan Chen ◽  
Hou-Duo Qi
Keyword(s):  
Symmetric Cones

Characterizations of symmetric cones by means of the basic relative invariants of homogeneous cones

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Hideto Nakashima
Keyword(s):  
Sufficient Conditions ◽  
Rational Functions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Symmetric Cones ◽  
The Real ◽  
Tube Domains ◽  
Homogeneous Cone ◽  
Necessary And Sufficient ◽  
Relative Invariants

AbstractIn this paper, we give necessary and sufficient conditions for a homogeneous cone Ω to be symmetric in two ways. One is by using the multiplier matrix of Ω, and the other is in terms of the basic relative invariants of Ω. In the latter approach, we need to show that the real parts of certain meromorphic rational functions obtained by the basic relative invariants are always positive on the tube domains over Ω. This is a generalization of a result of Ishi and Nomura [Math. Z. 259 (2008), 604–674].

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