Spectral representation theory for higher order nonlinear responses in random composites with arbitrary nonlinearity

2004 ◽  
Vol 241 (5) ◽  
pp. 1115-1123 ◽  
Author(s):  
Liping Gu ◽  
Lei Gao ◽  
Zhenya Li
Keyword(s):  
Representation Theory ◽  
Spectral Representation ◽  
Higher Order ◽  
Nonlinear Responses ◽  
Random Composites

scholarly journals Representation theory of the higher-order peak algebras

2010 ◽  
Vol 32 (4) ◽  
pp. 465-495 ◽  
Author(s):  
Jean-Christophe Novelli ◽  
Franco Saliola ◽  
Jean-Yves Thibon
Keyword(s):  
Representation Theory ◽  
Higher Order

Higher-order tensors, strings and new tensors

1990 ◽  
Vol 430 (1879) ◽  
pp. 423-432 ◽  
Keyword(s):  
Representation Theory ◽  
Higher Order ◽  
General Treatment ◽  
Infinite Dimensional ◽  
Dimensional Group ◽  
Group A ◽  
Higher Order Tensors

We consider a number of generalizations of tensors such as strings and new-tensors, of interest in particular in statistics. We give a general treatment of such objects and show that their properties can be described by the representation theory of an infinite-dimensional group. This group is defined and some of its representations examined. As there is no developed representation theory for this group a number of conjectures are made.

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).

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