Download PDF - A nilpotent Lie algebra and eigenvalue estimatesAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

A nilpotent Lie algebra and eigenvalue estimates

Authors 1, 1, 2

Affiliations

  1. Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
  2. Department of Mathematics and Statistics, The University at Albany/SUNY, Albany, New York 12222, U.S.A.

Abstract

The aim of this paper is to demonstrate how a fairly simple nilpotent Lie algebra can be used as a tool to study differential operators on ℝn with polynomial coefficients, especially when the property studied depends only on the degree of the polynomials involved and/or the number of variables.

Bibliography

  1. [Br] I. D. Brown, Dual topology of a nilpotent Lie group, Ann. Sci. École Normale Sup. (4) 6 (1973), 407-411.
  2. [Fe] C. L. Fefferman, The uncertainty principle, Bull. Amer. Math. Soc. 9 (1983), 129-206.
  3. [Fell] J. M. G. Fell, The dual spaces of C*-algebras, Trans. Amer. Math. Soc. 94 (1960), 365-403.
  4. [FS] G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Princeton Univ. Press, Princeton, N .J., 1982.
  5. [Gł] P. Głowacki, The Rockland condition for non-differential convolution operators, Duke Math. J. 58 (1989), 371-395.
  6. [HN] B. Helffer et J. Nourrigat, Caractérisation des opérateurs hypoelliptiques homogènes invariants à gauche sur un groupe gradué, Comm. Partial Differential Equations 4 (1978), 899-958.
  7. [HJ] A. Hulanicki and J. W. Jenkins, Nilpotent Lie groups and eigenfunction expansions of Schrödinger operators II, Studia Math. 87 (1987), 239-252.
  8. [HJL] A. Hulanicki, J. W. Jenkins and J. Ludwig, Minimum eigenvalues for positive Rockland operators, Proc. Amer. Math. Soc. 94 (1985), 718-720.
Colloquium Mathematicum
1995/68/1
Export to PBN, Opens in new tab
Pages:
7-16
Main language of publication
English
Received
1990-10-08
Accepted
1993-12-10
Published
1995
Exact and natural sciences