Green's functions of generalized Laplacians

被引：0
作者：
Poulin, Philippe
机构：
来源：
PROBABILITY AND MATHEMATICAL PHYSICS: A VOLUME IN HONOR OF STANISLAV MOLCHANOV | 2007年 / 42卷
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D O I：
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中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Green's function of a typical discrete Laplacian, Delta, in dimension d is given by G(n - m,z) = integral(Td) e(i(n-m)center dot x)/Phi(x) - z dx, where m,n is an element of Z(d), z is an element of C+, and Phi(x) is the symbol of Delta. Using the stationary phase method we study the decay of G(n, e + i0) when |n| -> infinity for values of energy, e, inside the range of Phi(x), where Phi(x) is analytic. We focus on two specific examples: the standard Laplacian and the Molchanov-Vainberg Laplacian.
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页码：417 / 452
页数：36
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