Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Concrete Operators

Ed. by Chalendar, Isabelle / Partington, Jonathan

1 Issue per year

Mathematical Citation Quotient (MCQ) 2016: 0.38

Emerging Science

Open Access
See all formats and pricing
More options …

On a space of entire functions rapidly decreasing on Rn and its Fourier transform

Il’dar Kh. Musin
  • Corresponding author
  • Institute of Mathematics with Computer Centre of RAS, Chernyshevsky str., 112, Ufa, 450077, Russia
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-11-06 | DOI: https://doi.org/10.1515/conop-2015-0007


A space of entire functions of several complex variables rapidly decreasing on Rn and such that their growth along iRn is majorized with the help of a family of weight functions is considered in this paper. For such space an equivalent description in terms of estimates on all of its partial derivatives as functions on Rn and a Paley-Wiener type theorem are obtained.

Keywords: Gelfand-Shilov spaces; Fourier transform; entire functions; convex functions


  • [1] Betancor J.J., Rodríguez-Mesa L., Characterizations of W-type spaces, Proc. Amer. Math. Soc., 1998, 126, 1371-1379 Google Scholar

  • [2] De Bruijn N.G., A theory of generalized functions, with applications toWigner distribution and Weyl correspondence, Nieuw Archief Wiskunde, 1973, 21, 205-280 Google Scholar

  • [3] Cho J., A characterization of Gelfand-Shilov space based on Winger distribution, Comm. Korean Math. Soc., 1999, 14, 761- 767 Google Scholar

  • [4] Chung J., Chung S.-Y., and Kim D., Characterizations of the Gelfand-Shilov spaces via Fourier transforms, Proc. Amer. Math. Soc., 1996, 124, 2101-2108 Google Scholar

  • [5] Chung J., Chung S.-Y., and Kim D., Equivalence of the Gelfand-Shilov spaces, Journal of Math. Anal. and Appl., 1996, 203, 828-839 Google Scholar

  • [6] Van Eijndhoven S.J.L., Kerkhof M.J., The Hankel transformation and spaces of type W, Reports on Applied and Numerical Analysis, Departament of Mathematics and Computing Science, Eindhoven University of Technology, 1988 Google Scholar

  • [7] Fainberg V.Ya., Soloviev M.A., Nonlocalizability and asymptotical commutativity, Theoretical and Mathematical Physics, 1992, 93, 1438-1449 Google Scholar

  • [8] Gelfand I.M., Shilov G.E., Generalized functions, Vol. 2, Academic Press, New York, 1968 Google Scholar

  • [9] Gelfand I.M., Shilov G.E., Generalized functions, Vol. 3, Academic Press, New York, 1967 Google Scholar

  • [10] Gurevich B.L., New types of spaces of fundamental and generalized functions and Cauchy’s problem for systems of finite difference equations, Doklady Akad. Nauk SSSR (N.S.), 1954, 99, 893-895, (in Russian). Google Scholar

  • [11] Gurevich B.L., New types of fundamental and generalized spaces and Cauchy’s problem for systems of difference equations involving differential operations, Doklady Akad. Nauk SSSR (N.S.), 1956, 108, 1001-1003, (in Russian). Google Scholar

  • [12] Janssen A.J.E.M., Van Eijndhoven S.J.L., Spaces of typeW, growth of Hermite coefficients,Wigner distribution and Bargmann transform, J. Math. Anal. Appl., 1990, 152, 368-390 Google Scholar

  • [13] Napalkov V.V., Popenov S.V., On Laplace transformation on weighted Bergman space of entire functions on Cn, Doklady Mathematics, 1997, 354, 595-597, (in Russian). Google Scholar

  • [14] Pathak R.S., On Hankel transformable spaces and a Cauchy problem, Can. J. Math., 1985, 37, 84-106 Google Scholar

  • [15] Pathak R.S., Upadhyay S.K., Wp-spaces and Fourier transform, Proc. Amer. Math. Soc., 1994, 121, 733-738 Google Scholar

  • [16] Rockafellar R.T., Convex analysis, Princeton, New Jersey, Princeton University Press, 1970 Google Scholar

  • [17] Upadhyay S.K., W-Spaces and Pseudo-differential Operators, Applicable Analysis, 2003, 82, 381-397 Web of ScienceGoogle Scholar

About the article

Received: 2015-07-15

Accepted: 2015-08-10

Published Online: 2015-11-06

Citation Information: Concrete Operators, Volume 2, Issue 1, ISSN (Online) 2299-3282, DOI: https://doi.org/10.1515/conop-2015-0007.

Export Citation

© 2015 Il’dar Kh. Musin. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in