Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Characterizations of the Gelfand-Shilov spaces via Fourier transforms
HTML articles powered by AMS MathViewer

by Jaeyoung Chung, Soon-Yeong Chung and Dohan Kim PDF
Proc. Amer. Math. Soc. 124 (1996), 2101-2108 Request permission

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
  • Jaeyoung Chung, Soon-Yeong Chung, and Dohan Kim, Une caractérisation de l’espace $\scr S$ de Schwartz, C. R. Acad. Sci. Paris Sér. I Math. 316 (1993), no. 1, 23–25 (French, with English and French summaries). MR 1198743
  • Jaeyoung Chung, Soon-Yeong Chung, and Dohan Kim, A characterization for Fourier hyperfunctions, Publ. Res. Inst. Math. Sci. 30 (1994), no. 2, 203–208. MR 1265470, DOI 10.2977/prims/1195166129
  • —, Equivalence of the Gelfand-Shilov spaces, J. Math. Anal. Appl., (to appear).
  • Soon-Yeong Chung and Dohan Kim, Representation of quasianalytic ultradistributions, Ark. Mat. 31 (1993), no. 1, 51–60. MR 1230264, DOI 10.1007/BF02559497
  • S.-Y. Chung, D. Kim, and S. K. Kim, Equivalence of the spaces of ultradifferentiable functions and its applications to Whitney extension theorem, Rend. Mat. Appl. (7) 12 (1992), no. 2, 365–380 (English, with English and Italian summaries). MR 1185897
  • I. M. Gel′fand and G. E. Shilov, Generalized functions. Vol. 1, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1964 [1977]. Properties and operations; Translated from the Russian by Eugene Saletan. MR 0435831
  • Lars Hörmander, A uniqueness theorem of Beurling for Fourier transform pairs, Ark. Mat. 29 (1991), no. 2, 237–240. MR 1150375, DOI 10.1007/BF02384339
  • A. I. Kashpirovsky, Equality of the spaces $S^{\beta }_{\alpha }$ and $S_{\alpha }\cap S^{\beta }$, Functional Anal. Appl. 14 (1978), 60.
  • Hikosaburo Komatsu, Ultradistributions. I. Structure theorems and a characterization, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 20 (1973), 25–105. MR 320743
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
  • 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 1996 American Mathematical Society
  • 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