Geodesic
Green function and Fourier transform for o-plus operators
Electronic journal of differential equations, Tome 2010 (2010)
In this article, we study the o-plus operator defined by

$ \oplus^k =\Big(\Big(\sum^{p}_{i=1}\frac{\partial^2}{\partial x^2_i}\Big)^{4}-\Big(\sum^{p+q}_{j=p+1}\frac{\partial^2}{\partial x^2_j}\Big)^{4}\Big)^k , $

where $x=(x_1,x_2,\dots,x_n)\in \mathbb{R}^n, p+q=n$, and $k$ is a nonnegative integer. Firstly, we studied the elementary solution for the $\oplus^k $ operator and then this solution is related to the solution of the wave and the Laplacian equations. Finally, we studied the Fourier transform of the elementary solution and also the Fourier transform of its convolution.
Classification : 46F10, 46F12
Keywords: Fourier transform, diamond operator, tempered distribution 
@article{EJDE_2010__2010__a7,
     author = {Satsanit,  Wanchak},
     title = {Green function and {Fourier} transform for o-plus operators},
     journal = {Electronic journal of differential equations},
     year = {2010},
     volume = {2010},
     zbl = {1202.46048},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a7/}
}
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Satsanit,  Wanchak. Green function and Fourier transform for o-plus operators. Electronic journal of differential equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a7/