Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

Characterizations of the Gelfand-Shilov spaces via Fourier transforms

Author(s): Jaeyoung Chung; Soon-Yeong Chung; Dohan Kim
Journal: Proc. Amer. Math. Soc. 124 (1996), 2101-2108.
MSC (1991): Primary 46F12, 46F15
MathSciNet review: 1322917
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

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.

References:

[1]: J. Chung, S. Y. Chung, and D. Kim, Une caractérisation de l'espace de Schwartz, C. R. Acad. Sci. Paris Sér. I Math. 316 (1993), 23--25. MR 93m:46040
[2]: ------, A characterization for Fourier hyperfunctions, Publ. RIMS, Kyoto Univ. 30 (1994), 203--208. MR 94m:46066
[3]: ------, Equivalence of the Gelfand-Shilov spaces, J. Math. Anal. Appl., (to appear).
[4]: S.-Y. Chung and D. Kim, Representation of quasianalytic ultradistributions, Ark. Mat. 31 (1993), 51--60. MR 94e:46069
[5]: S. Y. Chung, D. Kim, and S. K. Kim, Equivalence of the spaces of ultradifferentiable functions and its application to the Whitney extension theorem, Rend. Mat. Appl. VII 12 (1992), 365--380. MR 93k:46030
[6]: I. M. Gelfand and G. E. Shilov, Generalized functions II, III, Academic Press, New York and London, 1967. MR 55:8786c
[7]: L. Hörmander, A uniqueness theorem of Beurling for Fourier transform pairs, Ark. Mat. 29 (1991), 237--240. MR 93b:42016
[8]: A. I. Kashpirovsky, Equality of the spaces $S^{\beta }_{\alpha }$ and $S_{\alpha }\cap S^{\beta }$ , Functional Anal. Appl. 14 (1978), 60.
[9]: H. Komatsu, Ultradistributions I, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 20 (1973), 25--105. MR 47:9277

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46F12, 46F15

Retrieve articles in all Journals with MSC (1991): 46F12, 46F15

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: 10.1090/S0002-9939-96-03291-1
PII: S 0002-9939(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
Copyright of article: Copyright 1996, American Mathematical Society

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|