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Transactions of the American Mathematical Society

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

 

 

Hypoelliptic convolution equations in $ K'_p$, $ p>1$


Authors: G. Sampson and Z. Zieleźny
Journal: Trans. Amer. Math. Soc. 223 (1976), 133-154
MSC: Primary 46F10; Secondary 47G05
DOI: https://doi.org/10.1090/S0002-9947-1976-0425607-8
MathSciNet review: 0425607
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Abstract: We consider convolution equations in the space $ {K'_p},p > 1$, of distributions which ``grow'' no faster than $ \exp (k\vert x{\vert^p})$ for some constant k.

Our main result is a complete characterization of hypoelliptic convolution operators in $ {K'_p}$ in terms of their Fourier transforms.


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DOI: https://doi.org/10.1090/S0002-9947-1976-0425607-8
Article copyright: © Copyright 1976 American Mathematical Society