scholarly journals Strong hypercontractivity and logarithmic Sobolev inequalities on stratified complex Lie groups

2017 ◽  
Vol 370 (9) ◽  
pp. 6651-6683 ◽  
Author(s):  
Nathaniel Eldredge ◽  
Leonard Gross ◽  
Laurent Saloff-Coste
Keyword(s):  
Lie Groups ◽  
Sobolev Inequalities ◽  
Logarithmic Sobolev Inequalities

BEYOND STRONG SUBADDITIVITY? IMPROVED BOUNDS ON THE CONTRACTION OF GENERALIZED RELATIVE ENTROPY

1994 ◽  
Vol 06 (05a) ◽  
pp. 1147-1161 ◽  
Author(s):  
MARY BETH RUSKAI
Keyword(s):  
Relative Entropy ◽  
Discrete Case ◽  
Sobolev Inequalities ◽  
Completely Positive ◽  
Logarithmic Sobolev Inequalities ◽  
Strong Subadditivity

New bounds are given on the contraction of certain generalized forms of the relative entropy of two positive semi-definite operators under completely positive mappings. In addition, several conjectures are presented, one of which would give a strengthening of strong subadditivity. As an application of these bounds in the classical discrete case, a new proof of 2-point logarithmic Sobolev inequalities is presented in an Appendix.

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