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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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A characterization in the space of convolution operators
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by B. R. Nagaraj PDF
Proc. Amer. Math. Soc. 94 (1985), 396-398 Request permission

Abstract:

We give a characterization of ${C^\infty }$ elements in the space of convolution operators ${\theta ’_c}$, which belong to the Schwartz space $\mathcal {S}$.
References
    L. Hörmander, Linear partial differential operators, Grundleheren Math. Wiss., Vol. 116, Springer-Verlag, Berlin and New York, 1963.
  • Lars Hörmander, Pseudo-differential operators and hypoelliptic equations, Singular Integrals (Proc. Sympos. Pure Math., Chicago, Ill., 1966) Amer. Math. Soc., Providence, R.I., 1967, pp. 138–183. MR 0383152
  • Louis Nirenberg, Lectures on linear partial differential equations, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 17, American Mathematical Society, Providence, R.I., 1973. Expository Lectures from the CBMS Regional Conference held at the Texas Technological University, Lubbock, Tex., May 22–26, 1972. MR 0450755
  • Laurent Schwartz, Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, IX-X, Hermann, Paris, 1966 (French). Nouvelle édition, entiérement corrigée, refondue et augmentée. MR 0209834
  • François Trèves, Topological vector spaces, distributions and kernels, Academic Press, New York-London, 1967. MR 0225131
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 94 (1985), 396-398
  • MSC: Primary 46F10; Secondary 35S99
  • DOI: https://doi.org/10.1090/S0002-9939-1985-0787880-7
  • MathSciNet review: 787880