Domains of holomorphy for Fourier transforms of solutions to discrete convolution equations
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DOI: 10.1007/s11425-015-9029-0
Abstract: We study solutions to convolution equations for functions with discrete support in ℝn, a special case being functions with support in the integer points. The Fourier transform of a solution can be extended to a… read more here.
Keywords: transforms solutions; convolution equations; convolution; domains holomorphy ... See more keywords
On Mellin transforms of solutions of differential equation $$\chi ^{(n)}(x)+\gamma _{n}x\chi (x)=0$$ χ ( n ) ( x ) + γ n x χ ( x ) = 0
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DOI: 10.1007/s13324-020-00399-8
Abstract: In this paper, for $$ n=2,3,\ldots ,$$ n = 2 , 3 , … , we consider the differential equation $$\begin{aligned} \chi ^{(n)}(x)+\gamma _{n}x\chi (x)=0,\quad \left\{ \begin{array}{ll} \gamma _{n}=(-1)^{k},&{}\quad n=2k,\\ \gamma _{n}=-1,&{}\quad n=2k+1, \end{array}\right. \end{aligned}$$… read more here.
Keywords: differential equation; gamma chi; transforms solutions; mellin transforms ... See more keywords