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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the convolution equations in the space of distributions of $L^ p$-growth
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by D. H. Pahk PDF
Proc. Amer. Math. Soc. 94 (1985), 81-86 Request permission

Abstract:

We consider convolution equations in the space ${D’_{{L^p}}},\;1 \leqslant p \leqslant \infty$, of distributions of ${L^p}$-growth, i.e. distributions which are finite sums of derivatives of ${L^p}$-functions (see [4, 7]). Our main results are to find a condition for convolution operators to be hypoelliptic in ${\mathcal {D}’_{{L^\infty }}}$ 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 $\mathcal {S}’$ and ${\mathcal {D}’_{{L^p}}}$.
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • 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