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Proceedings of the American Mathematical Society

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Characterizations of the Gelfand-Shilov spaces
via Fourier transforms


Authors: Jaeyoung Chung, Soon-Yeong Chung and Dohan Kim
Journal: Proc. Amer. Math. Soc. 124 (1996), 2101-2108
MSC (1991): Primary 46F12, 46F15
DOI: https://doi.org/10.1090/S0002-9939-96-03291-1
MathSciNet review: 1322917
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Abstract: We give symmetric characterizations, with respect to the Fourier transformation, of the Gelfand-Shilov spaces of (generalized) type $S$ and type $W$. These results explain more clearly the invariance of these spaces under the Fourier transformations.


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Additional Information

Jaeyoung Chung
Affiliation: Department of Mathematics, Kunsan National University, Kunsan 573–360, Korea
Email: jychung@knusun1.kunsan.ac.kr

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

DOI: https://doi.org/10.1090/S0002-9939-96-03291-1
Keywords: Gelfand-Shilov spaces, Fourier transform, associated function
Received by editor(s): November 3, 1994
Received by editor(s) in revised form: January 26, 1995
Additional Notes: Partially supported by Korea Research Foundation and GARC.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society