Advertisement

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)

Abstract

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.

Keywords

Laplace Transformation Open Cone Common Domain Linear Partial Differential Equation Microlocal Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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

Personalised recommendations