Phase retrieval based on the irradiance transport equation and the Fourier transform method: experiments

1988 ◽  
Vol 27 (16) ◽  
pp. 3433 ◽  
Author(s):  
Kazuichi Ichikawa ◽  
Adolf W. Lohmann ◽  
Mitsuo Takeda
Keyword(s):  
Fourier Transform ◽  
Transport Equation ◽  
Phase Retrieval ◽  
Transform Method ◽  
Fourier Transform Method ◽  
The Fourier Transform

The interpretation of x-ray rocking curves by the Fourier transform method

1997 ◽  
Vol 30 (24) ◽  
pp. 3296-3300 ◽  
Author(s):  
M Li ◽  
M O Möller ◽  
H R Reß ◽  
W Faschinger ◽  
G Landwehr
Keyword(s):  
Fourier Transform ◽  
Transform Method ◽  
Fourier Transform Method ◽  
X Ray ◽  
The Fourier Transform

Poisson’s integral formula via heat kernels

Analysis ◽  
2019 ◽  
Vol 39 (2) ◽  
pp. 59-64
Author(s):  
Yoichi Miyazaki
Keyword(s):  
Fourier Transform ◽  
Heat Kernel ◽  
Half Space ◽  
Unbounded Domain ◽  
Harmonic Functions ◽  
Integral Formula ◽  
Heat Kernels ◽  
Transform Method ◽  
Fourier Transform Method ◽  
The Fourier Transform

Abstract We give another proof of Poisson’s integral formula for harmonic functions in a ball or a half space by using heat kernels with Green’s formula. We wish to emphasize that this method works well even for a half space, which is an unbounded domain; the functions involved are integrable, since the heat kernel decays rapidly. This method needs no trick such as the subordination identity, which is indispensable when applying the Fourier transform method for a half space.

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