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Continuation of functionals on ultradifferentiable function spaces

Продолжение функцио налов на пространств ах ультрадифференциру емых функций

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Abstract

Вводится продолжение функцио налов с пространства\(S_{c_k }^{^{a_q } }\) на\(S_{b_k }^{^{a_q } }\), гдеc k ⊂b k . Такие функционалы ха рактеризуются в терм инах их роста на бесконечнос ти. Исследуется также пр одолжение функциона лов в пространстве мульти пликаторов. Накладываются разли чные условия роста го ломорфных функций в трубчатых областях и исследует ся рост соответствую щих специальных функций.

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References

  1. K. I. Babenko, A new problem of quasi-analyticity and the Fourier transformations of entire functions (in Russian),Proc. Moscow Math. Soc.,5(1956), 523–542.

    Google Scholar 

  2. R. D. Carmichael andE. O. Milton, Distributional boundary values in the dual spaces of typeS, Pacific J. Math.,56(1975), 385–422.

    Google Scholar 

  3. I. M. Gel'fand andG. E. Shilov,Generalized functions, Vol. II, Academic Press (New York, 1964).

    Google Scholar 

  4. H. Komatsu, Ultradistributions. I: Structure theorems and a characterization,J. Fac. Sci. Univ. Tokyo Sect. IA Math.,20(1973), 25–105.

    Google Scholar 

  5. R. S. Pathak, Tempered ultradistributions as boundary values of analytic functions,Trans. Amer. Math. Soc.,286(1987), 537–556.

    Google Scholar 

  6. H. J. Petzsche, Die Nuklearität der Ultradistributions Räume und der Satz vom Kern. I,Manuscripta Math.,24(1978), 133–171.

    Article  Google Scholar 

  7. L. Schwartz,Théorie des distributions, Hermann (Paris, 1966).

    Google Scholar 

  8. C. Roumieu, Sur quelques extensions de la notion de distribution,Ann. Sci. École Norm. Sup., (3)77(1960), 41–121.

    Google Scholar 

  9. C. Roumieu, Ultra-distributions definies surR n et sur certaines classes de varieties differentiables,J. d'Analyse Math.,10 (1962/63), 153–192.

    Google Scholar 

  10. M. A. Solov'ev, The Fourier-Laplace transformation of generalized functions,Theoret. and Math. Phys.,15(1973), 317–328.

    Article  Google Scholar 

  11. V. S. Vladimirov,Methods of the theory of functions of many complex variables, M.I.T. Press (Cambridge, Mass., 1966).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Banaras Hindu University, 221 005, Varanasi, India

    R. S. Pathak

  2. Department of Mathematics, Rajshahi University, Bangladesh

    A. C. Paul

Authors
  1. R. S. Pathak
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  2. A. C. Paul
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Additional information

This work is supported by N.B.H.M. grant No. 48/1/94-R&D-II.

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Pathak, R.S., Paul, A.C. Continuation of functionals on ultradifferentiable function spaces. Analysis Mathematica 21, 177–190 (1995). https://doi.org/10.1007/BF01911124

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