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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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Characterization for Beurling-Björck space and Schwartz space
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by Soon-Yeong Chung, Dohan Kim and Sungjin Lee PDF
Proc. Amer. Math. Soc. 125 (1997), 3229-3234 Request permission

Abstract:

We give an elementary proof of the equivalence of the original definition of Schwartz and our characterization for the Schwartz space $\mathcal {S}$. The new proof is based on the Landau inequality concerning the estimates of derivatives. Applying the same method, as an application, we give a better symmetric characterization of the Beurling–Björck space of test functions for tempered ultradistributions with respect to Fourier transform without conditions on derivatives.
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Additional Information
  • Soon-Yeong Chung
  • Affiliation: Department of Mathematics, Sogang University, Seoul 121–742, Korea
  • Email: sychung@ccs.sogang.ac.kr
  • Dohan Kim
  • Affiliation: Department of Mathematics, Seoul National University, Seoul 151–742, Korea
  • Email: dhkim@math.snu.ac.kr
  • Sungjin Lee
  • Affiliation: Department of Mathematics, Daejin University, Pochun 487–800, Korea
  • Email: hyper@math.snu.ac.kr
  • Received by editor(s): December 11, 1995
  • Additional Notes: This work was partially supported by GARC–KOSEF and BSRI
  • Communicated by: J. Marshall Ash
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 3229-3234
  • MSC (1991): Primary 46F05, 46F12, 42B10
  • DOI: https://doi.org/10.1090/S0002-9939-97-04221-4
  • MathSciNet review: 1443817