Minimum eigenvalues for positive, Rockland operators
HTML articles powered by AMS MathViewer
- by A. Hulanicki, J. W. Jenkins and J. Ludwig
- Proc. Amer. Math. Soc. 94 (1985), 718-720
- DOI: https://doi.org/10.1090/S0002-9939-1985-0792290-2
- PDF | Request permission
Abstract:
Let $L$ be a positive, Rockland operator of homogeneous degree $\gamma$. The minimum eigenvalue of $d\pi (L)$ increases as the $\gamma$th power of the homogeneous distance from the origin of the orbit corresponding to $\pi$.References
- A. A. Kirillov, Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk 17 (1962), no. 4 (106), 57–110 (Russian). MR 0142001
- G. B. Folland and Elias M. Stein, Hardy spaces on homogeneous groups, Mathematical Notes, vol. 28, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1982. MR 657581
- B. Helffer and J. Nourrigat, Caracterisation des opérateurs hypoelliptiques homogènes invariants à gauche sur un groupe de Lie nilpotent gradué, Comm. Partial Differential Equations 4 (1979), no. 8, 899–958 (French). MR 537467, DOI 10.1080/03605307908820115
- Irving Kaplansky, The structure of certain operator algebras, Trans. Amer. Math. Soc. 70 (1951), 219–255. MR 42066, DOI 10.1090/S0002-9947-1951-0042066-0 J. Ludwig, G. Rosenbaum and J. Samuel, The elements of bounded trace in the ${C^*}$-algebra of a nilpotent Lie group (preprint).
- Edward Nelson and W. Forrest Stinespring, Representation of elliptic operators in an enveloping algebra, Amer. J. Math. 81 (1959), 547–560. MR 110024, DOI 10.2307/2372913 K. Yosida, Functional analysis, Springer, New York, 1965.
Bibliographic Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 94 (1985), 718-720
- MSC: Primary 22E30; Secondary 58G35
- DOI: https://doi.org/10.1090/S0002-9939-1985-0792290-2
- MathSciNet review: 792290