Roumieu Type Tempered Ultradistributions and Fourier Hyperfunctions

  • Atsuhiko Eida
  • Stevan Pilipović
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 7)


In [7] we studied spaces of tempered ultradifferential functions and tempered ultradistributions which are globally expressed for the usage of Fourier transforms on R n . These spaces S *, S '* are topologically automorphic to themselves through the Fourier transformation. On the other hand, Kawai and Kaneko have introduced the spaces of Fourier hyperfunctions which are homologically constructed on D n , the compactification of R n to the infinity (cf. [3] and [9]). These spaces are also topologically automorphic to themselves through the Fourier transformation.


Laplace Transformation Open Cone Common Domain Linear Partial Differential Equation Microlocal Analysis 
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  1. [1]
    R. Carmichael and S. Pilipović, On the convolution and Laplace transformation in the space of Beurling-Gevrey tempered ultradistributions, Math. Nachr., 158 (1992), 119–132.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    A. Eida and S. Pilipović, On the microlocal decomposition of some classes of ultradistributions, Math. Proc. Camb. Phil. Soc., 125 (1999), 455–461.MATHCrossRefGoogle Scholar
  3. [3]
    A.Kaneko, Introduction à la Théorie des Hyperfonctions I, II, Cours de DEA, Université de Grenoble (1978).Google Scholar
  4. [4]
    A. Kaneko, On the global existence of real analytic solutions of linear partial differential equations on unbounded domain, J. Fac. Sci., Univ. of Tokyo, Sect. IA 32 (1985), 319–372.MATHGoogle Scholar
  5. [5]
    H.Komatsu, Microlocal Analysis in Gevrey Classes and in Convex Domain, Springer, Lect. Not. Math. 1726 (1989), 426–493.Google Scholar
  6. [6]
    H.Komatsu, Structure theorems and a characterization, J. Fac. Sci., Univ. of Tokyo, Sect. IA 20 (1973), 25–105.MathSciNetMATHGoogle Scholar
  7. [7]
    D. Kovačevié and S. Pilipović, Structural properties of the space of tempered ultradistributions, Proc. Conf. “Complex Analysis and Generalized Functions”, Varna 1991, 169–184.Google Scholar
  8. [8]
    S. Pilipović, Characterization of bounded sets in spaces of ultradistributions, Proc. AMS, 120 (1994), 1191–1206.MATHGoogle Scholar
  9. [9]
    M.Sato, T.Kawai and M.Kashiwara, Microfunctions and pseudo-differential equations, Lect. Notes in Math. No 287 (1973), 265–529, Springer.MathSciNetGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Atsuhiko Eida
    • 1
  • Stevan Pilipović
    • 2
  1. 1.Faculty of Engineering ScienceTokyo University of TechnologyHachioji TokyoJapan
  2. 2.Institute of MathematicsUniversity of Novi SadNovi SadYugoslavia

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