A nilpotent Lie algebra and eigenvalue estimates

Jacek Dziubański; Andrzej Hulanicki; Joe Jenkins

Colloquium Mathematicae (1995)

  • Volume: 68, Issue: 1, page 7-16
  • ISSN: 0010-1354

Abstract

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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 ℝ n with polynomial coefficients, especially when the property studied depends only on the degree of the polynomials involved and/or the number of variables.

How to cite

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Dziubański, Jacek, Hulanicki, Andrzej, and Jenkins, Joe. "A nilpotent Lie algebra and eigenvalue estimates." Colloquium Mathematicae 68.1 (1995): 7-16. <http://eudml.org/doc/210297>.

@article{Dziubański1995,
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 $ℝ^n$ with polynomial coefficients, especially when the property studied depends only on the degree of the polynomials involved and/or the number of variables.},
author = {Dziubański, Jacek, Hulanicki, Andrzej, Jenkins, Joe},
journal = {Colloquium Mathematicae},
keywords = {Lie algebra; polynomials; unitary representation; Hilbert space; multiplication operator; unitary character; dilations; bounded measure; right convolution; gauge; Kirillov orbit; Riemann-Lebesgue lemma},
language = {eng},
number = {1},
pages = {7-16},
title = {A nilpotent Lie algebra and eigenvalue estimates},
url = {http://eudml.org/doc/210297},
volume = {68},
year = {1995},
}

TY - JOUR
AU - Dziubański, Jacek
AU - Hulanicki, Andrzej
AU - Jenkins, Joe
TI - A nilpotent Lie algebra and eigenvalue estimates
JO - Colloquium Mathematicae
PY - 1995
VL - 68
IS - 1
SP - 7
EP - 16
AB - 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 $ℝ^n$ with polynomial coefficients, especially when the property studied depends only on the degree of the polynomials involved and/or the number of variables.
LA - eng
KW - Lie algebra; polynomials; unitary representation; Hilbert space; multiplication operator; unitary character; dilations; bounded measure; right convolution; gauge; Kirillov orbit; Riemann-Lebesgue lemma
UR - http://eudml.org/doc/210297
ER -

References

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  1. [Br] I. D. Brown, Dual topology of a nilpotent Lie group, Ann. Sci. École Normale Sup. (4) 6 (1973), 407-411. Zbl0284.57026
  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. Zbl0090.32803
  4. [FS] G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Princeton Univ. Press, Princeton, N .J., 1982. Zbl0508.42025
  5. [Gł] P. Głowacki, The Rockland condition for non-differential convolution operators, Duke Math. J. 58 (1989), 371-395. Zbl0678.43002
  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. Zbl0423.35040
  7. [HJ] A. Hulanicki and J. W. Jenkins, Nilpotent Lie groups and eigenfunction expansions of Schrödinger operators II, Studia Math. 87 (1987), 239-252. Zbl0654.43004
  8. [HJL] A. Hulanicki, J. W. Jenkins and J. Ludwig, Minimum eigenvalues for positive Rockland operators, Proc. Amer. Math. Soc. 94 (1985), 718-720. Zbl0546.43008

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