Advertisement

Homogeneous generalized functions with respect to one-parametric group

  • Yu. N. DrozhzhinovEmail author
  • B. I. Zavialov
Research Articles

Abstract

We give the full description of homogeneous generalized functions along the trajectories of arbitrary one-parametric multiplicative group of linear transformations whose generator matrix has eigenvalues with positive real parts.We also study the problem of extension of such functionals from the space of test functions vanishing at the origin up to the whole space S(ℝ n ), and discuss the conditions of uniqueness of such extension.

Key words

generalized functions homogeneous functions quasiasymptotics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    I. M. Gel’fand and G. E. Shilov, Generalized Functions. Vol.I: Properties and Operations (Acad. Press, New York-London 1964).zbMATHGoogle Scholar
  2. 2.
    Yu. N. Drozhzhinov and B. I. Zavialov, “Generalized functions asymptotically homogeneous along special transformation groups,” Sb. Math. 200(6), 803–844 (2009).MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Yu. N. Drozhzhinov and B. I. Zavialov, “Asymptotically homogeneous generalized functions at zero and convolution equations with kernels quasi-homogeneous polynomial symbols,” Dokl. Math. 79(3), 356–359 (2009).MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Yu. N. Drozhzhinov and B. I. Zavialov, “Asymptotically homogeneous generalized functions and boundary properties of functions holomorphic in tubular cones,” Izv. Math. 70(6), 1117–1164 (2006).MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Yu. N. Drozhzhinov and B. I. Zavialov, “Generalized functions asymptotically homogeneous along the trajectory defined by one-parameter group,” Izv. RAN, ser. Math. 76(4), in print (2012).Google Scholar
  6. 6.
    E. Seneta, Regularly Varying Functions, Lecture Notes in Math. 508 (Springer-Verlag, Berlin-Heidelberg-New York, 1976).zbMATHCrossRefGoogle Scholar
  7. 7.
    V. S. Vladimirov, Yu. N. Drozhzhinov and B. I. Zavialov, Tauberian Theorems for Generalized Functions Translated fromthe Russian,Mathematics and its Applications (Soviet Series) 10 (Kluwer Acad. Publ. Group, Dordrecht, 1988).zbMATHGoogle Scholar
  8. 8.
    O. Grudzinski, Quazihomogeneous Distribution, North-Holland Math. Studies 165 (North-Holland-Amsterdam, 1991).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

Personalised recommendations