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

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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

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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

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  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). 
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  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
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  17. [17] Upadhyay S.K., W-Spaces and Pseudo-differential Operators, Applicable Analysis, 2003, 82, 381-397 Zbl1045.46021

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