scholarly journals Estimates for the complex Green operator: Symmetry, percolation, and interpolation

2018 ◽  
Vol 371 (3) ◽  
pp. 2003-2020 ◽  
Author(s):  
Séverine Biard ◽  
Emil J. Straube
Keyword(s):  
Green Operator

A generalisation of a theorem of O. Perron for semilinear evolution equations

2016 ◽  
Vol 160 (3) ◽  
pp. 379-399
Author(s):  
CIPRIAN PREDA
Keyword(s):  
Evolution Equations ◽  
Point Of View ◽  
Green Operator ◽  
Input Output ◽  
Test Function ◽  
Linear Evolution ◽  
Linear Homogeneous Differential Equation ◽  
The One ◽  
Test Function Method ◽  
Semilinear Evolution Equations

AbstractWe generalise a well-known result of O. Perron from the 30s that connects the asymptotic behavior of a linear homogeneous differential equation with the response of the inhomogeneous associated equation to a certain class of inhomogeneities (for this reason, Perron's result is also referred to as “input-output method”, “test function method” or “admissibility”).Our extension is twofold, on the one hand, through the means of a (non)linear evolution family, we deal with the mild solution of a nonautonomous semilinear evolution equation and on the other hand, we collect a very general class of inhomogeneities, eligible for a Perron-type approach in this case.From a technical point of view, the Perron input-output scenario is achieved here by using the Green operator.

SCATTERING PATH FORMALISM FOR THE PROPAGATION OF INTERACTING COMPOUNDS IN ORDERED AND DISORDERED MATERIALS

2000 ◽  
Vol 07 (03) ◽  
pp. 205-210 ◽  
Author(s):  
J. BERAKDAR
Keyword(s):  
Single Site ◽  
Disordered Materials ◽  
Green Operator ◽  
Many Body ◽  
Interacting Particles ◽  
Operator Approach ◽  
Compound A ◽  
Dynamical Properties ◽  
Transition Operators ◽  
Internal Evolution

This study presents a theoretical framework for the propagation of a compound consisting of N interacting particles in a multicenter potential. A novel Green operator approach is proposed that disentangles the geometrical and dynamical properties of the scatterers from the internal evolution of the projectile compound. Furthermore, the transition operator for the scattering from the multicenter potential is expanded in terms of many-body scattering path operators, which in turn are expressed in terms of single site transition operators that are amenable to computations. To deduce the correlated many-body Green operator of the scattering compound, a cumulative method is designed that reduces the problem to the evaluation of Green operators of systems with a reduced number of interacting particles. This is particularly useful for efficient calculations and encompasses the usual perturbative approaches.

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