scholarly journals Continuity of the solution mappings to parametric generalized non-weak vector Ky Fan inequalities

2017 ◽  
Vol 13 (2) ◽  
pp. 967-975
Author(s):  
Yangdong Xu ◽  
◽  
Shengjie Li ◽  
Keyword(s):  
Ky Fan Inequalities ◽  
Ky Fan ◽  
Weak Vector

scholarly journals Error bounds of regularized gap functions for nonmonotone Ky Fan inequalities

2020 ◽  
Vol 16 (3) ◽  
pp. 1261-1272
Author(s):  
Minghua Li ◽  
◽  
Chunrong Chen ◽  
Shengjie Li ◽  
Keyword(s):  
Error Bounds ◽  
Gap Functions ◽  
Ky Fan Inequalities ◽  
Regularized Gap Functions ◽  
Ky Fan

scholarly journals On the Continuity of the Integrated Density of States in the Disorder

2019 ◽  
Author(s):  
Mira Shamis
Keyword(s):  
Density Of States ◽  
Schrödinger Operators ◽  
Random Schrödinger Operators ◽  
Integrated Density Of States ◽  
Schrodinger Operators ◽  
Quantitative Form ◽  
Alternative Approach ◽  
Ky Fan Inequalities ◽  
Ky Fan ◽  
Sharp Version

Abstract Recently, Hislop and Marx studied the dependence of the integrated density of states on the underlying probability distribution for a class of discrete random Schrödinger operators and established a quantitative form of continuity in weak* topology. We develop an alternative approach to the problem, based on Ky Fan inequalities, and establish a sharp version of the estimate of Hislop and Marx. We also consider a corresponding problem for continual random Schrödinger operators on $\mathbb{R}^d$.

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