Hypoelliptic convolution equations in the space 𝒦’ₑ

Pahk, Dae Hyeon

doi:10.1090/S0002-9947-1986-0860376-5

Hypoelliptic convolution equations in the space ${\scr K}’_ e$
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Trans. Amer. Math. Soc. 298 (1986), 485-495 Request permission

Abstract:

We consider convolution equations in the space $\mathcal {K}_e’$ of distributions which "grow" no faster than $\exp ({e^{k|x|}})$ 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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