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

Il’dar Kh. Musin

Concrete Operators (2015)

  • Volume: 2, Issue: 1, page 120-138, electronic only
  • ISSN: 2299-3282

Abstract

top
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.

How to cite

top

Il’dar Kh. Musin. "On a space of entire functions rapidly decreasing on Rn and its Fourier transform." Concrete Operators 2.1 (2015): 120-138, electronic only. <http://eudml.org/doc/275966>.

@article{Il2015,
abstract = {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.},
author = {Il’dar Kh. Musin},
journal = {Concrete Operators},
keywords = {Gelfand-Shilov spaces; Fourier transform; entire functions; convex functions},
language = {eng},
number = {1},
pages = {120-138, electronic only},
title = {On a space of entire functions rapidly decreasing on Rn and its Fourier transform},
url = {http://eudml.org/doc/275966},
volume = {2},
year = {2015},
}

TY - JOUR
AU - Il’dar Kh. Musin
TI - On a space of entire functions rapidly decreasing on Rn and its Fourier transform
JO - Concrete Operators
PY - 2015
VL - 2
IS - 1
SP - 120
EP - 138, electronic only
AB - 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.
LA - eng
KW - Gelfand-Shilov spaces; Fourier transform; entire functions; convex functions
UR - http://eudml.org/doc/275966
ER -

References

top
  1. [1] Betancor J.J., Rodríguez-Mesa L., Characterizations of W-type spaces, Proc. Amer. Math. Soc., 1998, 126, 1371-1379 Zbl0892.46042
  2. [2] De Bruijn N.G., A theory of generalized functions, with applications toWigner distribution and Weyl correspondence, Nieuw Archief Wiskunde, 1973, 21, 205-280 
  3. [3] Cho J., A characterization of Gelfand-Shilov space based on Winger distribution, Comm. Korean Math. Soc., 1999, 14, 761- 767 Zbl1026.46025
  4. [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 Zbl0871.46018
  5. [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 Zbl0892.46038
  6. [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 
  7. [7] Fainberg V.Ya., Soloviev M.A., Nonlocalizability and asymptotical commutativity, Theoretical and Mathematical Physics, 1992, 93, 1438-1449 
  8. [8] Gelfand I.M., Shilov G.E., Generalized functions, Vol. 2, Academic Press, New York, 1968 
  9. [9] Gelfand I.M., Shilov G.E., Generalized functions, Vol. 3, Academic Press, New York, 1967 
  10. [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). 
  11. [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). Zbl0073.31501
  12. [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 Zbl0749.46027
  13. [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). Zbl0985.46012
  14. [14] Pathak R.S., On Hankel transformable spaces and a Cauchy problem, Can. J. Math., 1985, 37, 84-106 Zbl0586.46035
  15. [15] Pathak R.S., Upadhyay S.K., Wp-spaces and Fourier transform, Proc. Amer. Math. Soc., 1994, 121, 733-738 Zbl0816.46033
  16. [16] Rockafellar R.T., Convex analysis, Princeton, New Jersey, Princeton University Press, 1970 Zbl0193.18401
  17. [17] Upadhyay S.K., W-Spaces and Pseudo-differential Operators, Applicable Analysis, 2003, 82, 381-397 Zbl1045.46021

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.