On the convolution equations in the space of distributions of -growth

Author:
D. H. Pahk

Journal:
Proc. Amer. Math. Soc. **94** (1985), 81-86

MSC:
Primary 46F10; Secondary 35H05, 46F05

DOI:
https://doi.org/10.1090/S0002-9939-1985-0781061-9

MathSciNet review:
781061

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Abstract: We consider convolution equations in the space , of distributions of -growth, i.e. distributions which are finite sums of derivatives of -functions (see [**4, 7**]). Our main results are to find a condition for convolution operators to be hypoelliptic in in terms of their Fourier transforms and to show that the same condition is working for the solvability of convolution operators in the tempered distribution space and .

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DOI:
https://doi.org/10.1090/S0002-9939-1985-0781061-9

Article copyright:
© Copyright 1985
American Mathematical Society