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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. ZieleĆșny
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 $\exp (k|x{|^p})$ 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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Article copyright: © Copyright 1976 American Mathematical Society