Weyl’s Theorem for Functions of Operators and Approximation

2010 ◽  
Vol 67 (4) ◽  
pp. 481-497 ◽  
Author(s):  
Chun Guang Li ◽  
Sen Zhu ◽  
You Ling Feng
Keyword(s):  
Weyl’S Theorem ◽  
Functions Of Operators

On Weyl’s Theorem for Functions of Operators

2019 ◽  
Vol 35 (8) ◽  
pp. 1367-1376
Author(s):  
Jiong Dong ◽  
Xiao Hong Cao ◽  
Lei Dai
Keyword(s):  
Weyl’S Theorem ◽  
Functions Of Operators

scholarly journals Weyl's theorem and its perturbations for the functions of operators

2018 ◽  
pp. 1145-1157
Author(s):  
Xiaoh ng Cao ◽  
Jiong Dong ◽  
Jun ui Liu
Keyword(s):  
Weyl’S Theorem ◽  
Functions Of Operators

Polarization of Separating Invariants

2008 ◽  
Vol 60 (3) ◽  
pp. 556-571 ◽  
Author(s):  
Jan Draisma ◽  
Gregor Kemper ◽  
David Wehlau
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Group Actions ◽  
Upper Bounds ◽  
Weyl’S Theorem ◽  
Finite Group Actions ◽  
Separating Invariants ◽  
The Difference ◽  
Special Case

AbstractWe prove a characteristic free version of Weyl’s theorem on polarization. Our result is an exact analogue ofWeyl’s theorem, the difference being that our statement is about separating invariants rather than generating invariants. For the special case of finite group actions we introduce the concept of cheap polarization, and show that it is enough to take cheap polarizations of invariants of just one copy of a representation to obtain separating vector invariants for any number of copies. This leads to upper bounds on the number and degrees of separating vector invariants of finite groups.

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