# 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

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topDziubański, 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

top- [Br] I. D. Brown, Dual topology of a nilpotent Lie group, Ann. Sci. École Normale Sup. (4) 6 (1973), 407-411. Zbl0284.57026
- [Fe] C. L. Fefferman, The uncertainty principle, Bull. Amer. Math. Soc. 9 (1983), 129-206.
- [Fell] J. M. G. Fell, The dual spaces of C*-algebras, Trans. Amer. Math. Soc. 94 (1960), 365-403. Zbl0090.32803
- [FS] G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Princeton Univ. Press, Princeton, N .J., 1982. Zbl0508.42025
- [Gł] P. Głowacki, The Rockland condition for non-differential convolution operators, Duke Math. J. 58 (1989), 371-395. Zbl0678.43002
- [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
- [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
- [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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