A nilpotent Lie algebra and eigenvalue estimates

• Autorzy: Jacek Dziubański , Andrzej Hulanicki , Joe Jenkins
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1995
• Tom: 68
• Numer: 1
• Strony: 7-16

Daty

wydano

1995

otrzymano

1990-10-08

poprawiono

1993-12-10

Twórcy

autor

Jacek Dziubański

• Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Andrzej Hulanicki

• Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Joe Jenkins

• Department of Mathematics and Statistics, The University at Albany/SUNY, Albany, New York 12222, U.S.A.

Bibliografia

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• [Fell] J. M. G. Fell, The dual spaces of C*-algebras, Trans. Amer. Math. Soc. 94 (1960), 365-403.
• [FS] G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Princeton Univ. Press, Princeton, N .J., 1982.
• [Gł] P. Głowacki, The Rockland condition for non-differential convolution operators, Duke Math. J. 58 (1989), 371-395.
• [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.
• [HJ] A. Hulanicki and J. W. Jenkins, Nilpotent Lie groups and eigenfunction expansions of Schrödinger operators II, Studia Math. 87 (1987), 239-252.
• [HJL] A. Hulanicki, J. W. Jenkins and J. Ludwig, Minimum eigenvalues for positive Rockland operators, Proc. Amer. Math. Soc. 94 (1985), 718-720.