Skip to main content
Log in

On a representation of smooth invariants of Coxeter groups in terms of anisotropic spaces

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

A smooth function invariant under the action of the Coxeter group can be represented as a function of basic invariants. We propose to describe the latter in terms of special anisotropic spaces, which enables us to obtain more precise estimates of its smoothness.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. G. Barbancon, “Théoréme de Newton pour les fonctions de classe C r”, Ann. Sci. Ecole. Norm. Super., Ser. 4 5, 435–438 (1972).

    MATH  MathSciNet  Google Scholar 

  2. J. M. Ball, “Differentiability properties of symmetric and isotropic functions”, Duke Math. J., 51, No. 3, 699–728 (1984).

    Article  MATH  MathSciNet  Google Scholar 

  3. G. Barbancon, “Invariants de classe C r des groupes finis engendres par des reflexions et theoreme de Chevalley en classe C r,” Duke Math. J., 53, No. 3, 563–584 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  4. A. O. Gokhman, “Smooth symmetric functions,” Ukr. Mat. Zh., 41, No. 6, 743–750 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  5. A. O. Gokhman, “On smooth functions invariant under groups generated by reflections” Mat. Zametki, 53, No. 4, 146–147 (1993).

    MATH  MathSciNet  Google Scholar 

  6. A. O. Gokhman, “On reduction of smoothness in the theorem on differentiable invariants of Coxeter groups,” Funk. Analiz. Prilozh., 28, No. 4, 82–84 (1994).

    MathSciNet  Google Scholar 

  7. A. O. Gokhman, On the Newton Theorem for Smooth Functions [in Russian], Dep. VINITI No. 8102-84, Moscow (1984).

Download references

Authors

Additional information

Voronezh University, Voronezh, Russia. Translated from Ukrainskii Matematicheskii Zhurnal Vol. 49, No. 4, pp. 597–600, April, 1997.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gokhman, A.O. On a representation of smooth invariants of Coxeter groups in terms of anisotropic spaces. Ukr Math J 49, 661–664 (1997). https://doi.org/10.1007/BF02487330

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02487330

Keywords

Navigation