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

Concrete Operators (2015)

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

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topIl’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] Betancor J.J., Rodríguez-Mesa L., Characterizations of W-type spaces, Proc. Amer. Math. Soc., 1998, 126, 1371-1379 Zbl0892.46042
- [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] Cho J., A characterization of Gelfand-Shilov space based on Winger distribution, Comm. Korean Math. Soc., 1999, 14, 761- 767 Zbl1026.46025
- [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] 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] 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] Fainberg V.Ya., Soloviev M.A., Nonlocalizability and asymptotical commutativity, Theoretical and Mathematical Physics, 1992, 93, 1438-1449
- [8] Gelfand I.M., Shilov G.E., Generalized functions, Vol. 2, Academic Press, New York, 1968
- [9] Gelfand I.M., Shilov G.E., Generalized functions, Vol. 3, Academic Press, New York, 1967
- [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] 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] 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] 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] Pathak R.S., On Hankel transformable spaces and a Cauchy problem, Can. J. Math., 1985, 37, 84-106 Zbl0586.46035
- [15] Pathak R.S., Upadhyay S.K., Wp-spaces and Fourier transform, Proc. Amer. Math. Soc., 1994, 121, 733-738 Zbl0816.46033
- [16] Rockafellar R.T., Convex analysis, Princeton, New Jersey, Princeton University Press, 1970 Zbl0193.18401
- [17] Upadhyay S.K., W-Spaces and Pseudo-differential Operators, Applicable Analysis, 2003, 82, 381-397 Zbl1045.46021

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