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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Hypoelliptic convolution equations in the space $ {\scr K}'\sb e$


Author: Dae Hyeon Pahk
Journal: Trans. Amer. Math. Soc. 298 (1986), 485-495
MSC: Primary 35H05; Secondary 35D99, 46F10
DOI: https://doi.org/10.1090/S0002-9947-1986-0860376-5
MathSciNet review: 860376
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Abstract: We consider convolution equations in the space $ \mathcal{K}_e' $ of distributions which "grow" no faster than $ \exp ({e^{k\vert x\vert}})$ for some constant $ k$. Our main results are to find conditions for convolution operators to be hypoelliptic in $ \mathcal{K}_e'$ in terms of their Fourier transforms.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0860376-5
Article copyright: © Copyright 1986 American Mathematical Society

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