Multipliers, Convolutors and Hypoelliptic Convolutors for Tempered Ultradistributions

  • Stevan Pilipović

Abstract

Malgrange’s, Ehrenpreis’s and Hörmander’s results on the solvability and the hy-poellipticity of convolution equations in Schwartz’s spaces of distributions stimulated many mathematicians to study such problems in various subspaces of distributions. We cite here only the results of Zielezny ([15], [16]) and Swartz ([12], [13]), since they are connected with the results of this paper. Convolution equations for ultradistribution spaces were studied by Meise, Taylor, Voigt and their cooperators; (see [1], [7] and references there.)

Keywords

Convolution Radon Novi 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R.W. Braun, R. Meise, D. Vogt, Existence of fundanemal solutions and surjecivity of convolution operators on class of ultradifferentiable functions, Proc. London Math. Soc. (3)6 (1990), 344–370.MathSciNetCrossRefGoogle Scholar
  2. [2]
    A. Kaminski, D. Kovačević, S. Pilipovic, On the Convolution of Ultradistributions, preprint.Google Scholar
  3. [3]
    H. Komatsu, Ultradistributions, I ; Strucure theorems and a characterizaion, J. Fac. Sci. Univ. Tokyo, Sect. IA Math. 20 (1973), 25–105.MathSciNetMATHGoogle Scholar
  4. [4]
    H. Komatsu, Microlocal Analysis in Gevrey Class and in Complex Domains, preprint.Google Scholar
  5. [5]
    D.Kovačević, Some operations on the space S’ (Mp) of tempered ultradistributions, Univ. u Novom Sadu, Zb. Rad. Prirod.- Mat. Fak. Ser. Mat. to appear.Google Scholar
  6. [6]
    D.Kovačević, S. Pilipovic, Structural properties of the space of tempered ultradistributions, Proc. Conf. Complex Analysis and Applications ’91 with Symposium on Generalized Functions, Varna 1991, to appear.Google Scholar
  7. [7]
    R. Miese, K. Schwerdfeger, B.A. Taylor, On Kernels of Slowly decreasing convolution operators, DOGA Tr. J.Math. 10, 1 (1986).Google Scholar
  8. [8]
    A. Pietsch, Nukleare lokalkonvexe Raume, Akademie- Verlag, Berlin, 1965.Google Scholar
  9. [9]
    S. Pilipovic, Tempered Ultradistributions, Bul. Un. Math. Ital. (7) 2-B (1988).Google Scholar
  10. [10]
    S.Pilipovic, Characterizations of ultradistributions spaces and bounded sets, preprint.Google Scholar
  11. [11]
    H. Shaefer, Topological vector spaces, Collier- Mac - Millan, London, 1986.Google Scholar
  12. [12]
    C. Swartz, Convergence of convolution operators, Studia Math. XLII (1972), 249–257.MathSciNetGoogle Scholar
  13. [13]
    C. Swartz, Convolution in K{MP} spaces, Rocky Monntain J. Math. 2 (1972), 259–263.MathSciNetMATHGoogle Scholar
  14. [14]
    J. Uryga, On tensor product and convoluion of generalized functions of Gelfand -Shilov type, Generalized Functions and Convergence, Memorial Volume for Prof. J. Mikusinski, World Scientific Singapore, Ed. A. Antosik, A.Kaminski, 251–264.Google Scholar
  15. [15]
    Z. Zielezny, Hipoelliptic and enire elliptic convolution equations in subspaces of the space of distributions (II), Sudia Math. XXXII (1969), 47–59.MathSciNetGoogle Scholar
  16. [16]
    Z. Zielezny, Hipoelliptic and entire elliptic convolution equations in subspaces of the space of disribuions (I), Studia Math. XXVIII (1967), 317–332.MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Stevan Pilipović
    • 1
  1. 1.Instiute of MathematicsUniversity of Novi SadNovi SadYugoslavia

Personalised recommendations