Retrieval of dielectric and structural properties of amorphous SiO2 nanopowder based on optical measurements and Bergman's spectral representation theory

2019 ◽  
Vol 126 (10) ◽  
pp. 104304
Author(s):  
Alima Nzie ◽  
Cédric Blanchard ◽  
Cécile Genevois ◽  
Domingos De Sousa Meneses
Keyword(s):  
Representation Theory ◽  
Structural Properties ◽  
Spectral Representation ◽  
Optical Measurements ◽  
Amorphous Sio2 ◽  
Sio2 Nanopowder

scholarly journals Stratifications and Mackey Functors II: Globally Defined Mackey Functors

2010 ◽  
Vol 6 (1) ◽  
pp. 99-170 ◽  
Author(s):  
Peter Webb
Keyword(s):  
Representation Theory ◽  
Structural Properties ◽  
Characteristic Zero ◽  
Group Representation ◽  
Cartan Matrix ◽  
Weight Category ◽  
Group Representation Theory ◽  
Stratification Theory ◽  
Highest Weight ◽  
Mackey Functors

AbstractWe describe structural properties of globally defined Mackey functors related to the stratification theory of algebras. We show that over a field of characteristic zero they form a highest weight category and we also determine precisely when this category is semisimple. This approach is used to show that the Cartan matrix is often symmetric and non-singular, and we are able to compute finite parts of it in some instances. We also develop a theory of vertices of globally defined Mackey functors in the spirit of group representation theory, as well as giving information about extensions between simple functors.

scholarly journals Self adjoint operators and matrix measures

1971 ◽  
Vol 4 (3) ◽  
pp. 289-305 ◽  
Author(s):  
Patrick J. Browne
Keyword(s):  
Hilbert Space ◽  
Representation Theory ◽  
Spectral Representation ◽  
Adjoint Operator ◽  
Multiplication Operator ◽  
Linear Operators ◽  
Positive Matrix ◽  
Adjoint Operators ◽  
Matrix Measures

Given a self adjoint operator, T, on a Hilbert space H, and given an integer n ≥ 1, we produce a collection , N ∈ L, of n × n positive matrix measures and a unitary map U: such that UTU−1, restricted to the co-ordinate space , is the multiplication operator F(t) → tF(t) in that space. This is a generalization of the spectral representation theory of Dunford and Schwartz, Linear operators, II (1966).

Sign in / Sign up

Export Citation Format

Share Document