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.References
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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