scholarly journals Computing Diffusion State Distance Using Green’s Function and Heat Kernel on Graphs

2014 ◽  
pp. 79-95 ◽  
Author(s):  
Edward Boehnlein ◽  
Peter Chin ◽  
Amit Sinha ◽  
Linyuan Lu
Keyword(s):  
Green’S Function ◽  
Heat Kernel ◽  
Green's Function ◽  
Diffusion State

The Heat Kernel and Green's Function on a Manifold with Heisenberg Group as Boundary

2004 ◽  
Vol 56 (3) ◽  
pp. 590-611
Author(s):  
Yilong Ni
Keyword(s):  
Riemannian Manifold ◽  
Heisenberg Group ◽  
Green’S Function ◽  
Heat Kernel ◽  
Green's Function ◽  
Beltrami Operator ◽  
Small Time ◽  
Time Estimates

AbstractWe study the Riemannian Laplace-Beltrami operator L on a Riemannian manifold with Heisenberg group H1 as boundary. We calculate the heat kernel and Green's function for L, and give global and small time estimates of the heat kernel. A class of hypersurfaces in this manifold can be regarded as approximations of H1. We also restrict L to each hypersurface and calculate the corresponding heat kernel and Green's function. We will see that the heat kernel and Green's function converge to the heat kernel and Green's function on the boundary.

Estimates on the Green's function of second-order elliptic operators in ℝN

1998 ◽  
Vol 128 (5) ◽  
pp. 1033-1051
Author(s):  
Adrian T. Hill
Keyword(s):  
Green’S Function ◽  
Heat Kernel ◽  
Hypergeometric Function ◽  
Green's Function ◽  
Confluent Hypergeometric Function ◽  
Elliptic Operators ◽  
Polar Coordinates ◽  
Pointwise Estimates ◽  
Image Position ◽  
Second Order Elliptic Operators

Sharp upper and lower pointwise bounds are obtained for the Green's function of the equationfor λ> 0. Initially, in a Cartesian frame, it is assumed that . Pointwise estimates for the heat kernel of ut + Lu = 0, recently obtained under this assumption, are Laplace-transformed to yield corresponding elliptic results. In a second approach, the coordinate-free constraint is imposed. Within this class of operators, the equations defining the maximal and minimal Green's functions are found to be simple ODEs when written in polar coordinates, and these are soluble in terms of the singular Kummer confluent hypergeometric function. For both approaches, bounds on are derived as a consequence.

scholarly journals Discrete heat kernel, UV modified Green's function, and higher derivative theories

2021 ◽  
Author(s):  
Nahomi Kan ◽  
Masashi Kuniyasu ◽  
Kiyoshi Shiraishi ◽  
Zhenyuan Wu
Keyword(s):  
Green’S Function ◽  
Heat Kernel ◽  
Green's Function ◽  
Higher Derivative

scholarly journals Sharp bounds for the Green’s function and the heat kernel

1997 ◽  
Vol 4 (4) ◽  
pp. 589-602 ◽  
Author(s):  
Peter Li ◽  
Luen-fai Tam ◽  
Jiaping Wang
Keyword(s):  
Green’S Function ◽  
Heat Kernel ◽  
Green's Function ◽  
Sharp Bounds

GREEN'S FUNCTION MATCHING METHOD FOR REALISTIC CALCULATIONS OF INTERFACES

1985 ◽  
Vol 46 (C4) ◽  
pp. C4-321-C4-329 ◽  
Author(s):  
E. Molinari ◽  
G. B. Bachelet ◽  
M. Altarelli
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Matching Method

THE ATOMISTIC GREEN'S FUNCTION METHOD FOR INTERFACIAL PHONON TRANSPORT

2014 ◽  
Vol 17 (N/A) ◽  
pp. 89-145 ◽  
Author(s):  
Sridhar Sadasivam ◽  
Yuhang Che ◽  
Zhen Huang ◽  
Liang Chen ◽  
Satish Kumar ◽  
...  
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Phonon Transport ◽  
Green’S Function Method
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