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Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2015-07-15
zaakceptowano
2015-08-10
online
2015-11-06
Twórcy
  • Institute of Mathematics with Computer Centre of RAS, Chernyshevsky str., 112,
    Ufa, 450077, Russia
Bibliografia
  • [1] Betancor J.J., Rodríguez-Mesa L., Characterizations of W-type spaces, Proc. Amer. Math. Soc., 1998, 126, 1371-1379
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  • [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
  • [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
  • [6] Van Eijndhoven S.J.L., Kerkhof M.J., The Hankel transformation and spaces of type W, Reports on Applied and NumericalAnalysis, Departament of Mathematics and Computing Science, Eindhoven University of Technology, 1988
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  • [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 finitedifference 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 equationsinvolving differential operations, Doklady Akad. Nauk SSSR (N.S.), 1956, 108, 1001-1003, (in Russian).
  • [12] Janssen A.J.E.M., Van Eijndhoven S.J.L., Spaces of typeW, growth of Hermite coefficients,Wigner distribution and Bargmanntransform, J. Math. Anal. Appl., 1990, 152, 368-390
  • [13] Napalkov V.V., Popenov S.V., On Laplace transformation on weighted Bergman space of entire functions on Cn, DokladyMathematics, 1997, 354, 595-597, (in Russian).
  • [14] Pathak R.S., On Hankel transformable spaces and a Cauchy problem, Can. J. Math., 1985, 37, 84-106
  • [15] Pathak R.S., Upadhyay S.K., Wp-spaces and Fourier transform, Proc. Amer. Math. Soc., 1994, 121, 733-738
  • [16] Rockafellar R.T., Convex analysis, Princeton, New Jersey, Princeton University Press, 1970
  • [17] Upadhyay S.K., W-Spaces and Pseudo-differential Operators, Applicable Analysis, 2003, 82, 381-397
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_conop-2015-0007
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