The Fourier Transform Method for Second-Order Integro-Dynamic Equations on Time Scales

2021 ◽  
Author(s):  
Svetlin G. Georgiev
Keyword(s):  
Fourier Transform ◽  
Time Scales ◽  
Second Order ◽  
Dynamic Equations ◽  
Transform Method ◽  
Fourier Transform Method ◽  
Arbitrary Time ◽  
The Fourier Transform

In this chapter we introduce the Fourier transform on arbitrary time scales and deduct some of its properties. In the chapter are given some applications for second-order integro-dynamic equations on time scales.

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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