Duke Mathematical Journal

The Rockland condition for nondifferential convolution operators

Paweł Głowacki

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Article information

Source
Duke Math. J., Volume 58, Number 2 (1989), 371-395.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077307530

Digital Object Identifier
doi:10.1215/S0012-7094-89-05817-1

Mathematical Reviews number (MathSciNet)
MR1016426

Zentralblatt MATH identifier
0678.43002

Subjects
Primary: 43A05: Measures on groups and semigroups, etc.
Secondary: 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX]

Citation

Głowacki, Paweł. The Rockland condition for nondifferential convolution operators. Duke Math. J. 58 (1989), no. 2, 371--395. doi:10.1215/S0012-7094-89-05817-1. https://projecteuclid.org/euclid.dmj/1077307530


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References

  • [1] H. Byczkowska and A. Hulanicki, On the support of the measures in a semigroup of probability measures on a locally compact group, Martingale theory in harmonic analysis and Banach spaces (Cleveland, Ohio, 1981), Lecture Notes in Math., vol. 939, Springer, Berlin, 1982, pp. 13–17.
  • [2] M. Christ and D. Geller, Singular integral characterizations of Hardy spaces on homogeneous groups, Duke Math. J. 51 (1984), no. 3, 547–598.
  • [3] W. Cupala, Certain Schrödinger operators as images of sublaplacians on nilpotent Lie groups, Ph.D. thesis, Institute of Mathematics, Polish Academy of Sciences, 1984.
  • [4] M. Duflo, Représentations de semi-groupes de mesures sur un groupe localement compact, Ann. Inst. Fourier (Grenoble) 28 (1978), no. 3, xii, 225–249.
  • [5] C. L. Fefferman, The uncertainty principle, Bull. Amer. Math. Soc. (N.S.) 9 (1983), no. 2, 129–206.
  • [6] G. B. Folland, Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat. 13 (1975), no. 2, 161–207.
  • [7] G. B. Folland and E. M. Stein, Hardy spaces on homogeneous groups, Mathematical Notes, vol. 28, Princeton University Press, Princeton, N.J., 1982.
  • [8] P. Głowacki, Stable semigroups of measures on the Heisenberg group, Studia Math. 79 (1984), no. 2, 105–138.
  • [9] P. Głowacki, Stable semigroups of measures as commutative approximate identities on nongraded homogeneous groups, Invent. Math. 83 (1986), no. 3, 557–582.
  • [10] P. Głowacki, The Rockland condition for nondifferential convolution operators. II, Studia Math. 98 (1991), no. 2, 99–114.
  • [11] P. Głowacki and A. Hulanicki, A semigroup of probability measures with nonsmooth differentiable densities on a Lie group, Colloq. Math. 51 (1987), 131–139.
  • [12] B. Helffer and F. Nourrigat, Hypoellipticité pour des groupes nilpotents de rang de nilpotence $3$, Comm. Partial Differential Equations 3 (1978), no. 8, 643–743.
  • [13] 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.
  • [14] H. Heyer, Probability measures on locally compact groups, Springer-Verlag, Berlin, 1977.
  • [15] A. Hulanicki, A class of convolution semigroups of measures on a Lie group, Probability theory on vector spaces, II (Proc. Second Internat. Conf., Błażejewko, 1979), Lecture Notes in Math., vol. 828, Springer, Berlin, 1980, pp. 82–101.
  • [16] A. Hulanicki and J. W. Jenkins, Nilpotent Lie groups and summability of eigenfunction expansions of Schrödinger operators, Studia Math. 80 (1984), no. 3, 235–244.
  • [17] A. Hulanicki and J. W. Jenkins, Nilpotent Lie groups and eigenfunction expansions of Schrödinger operators. II, Studia Math. 87 (1987), no. 3, 239–252.
  • [18] G. A. Hunt, Semi-groups of measures on Lie groups, Trans. Amer. Math. Soc. 81 (1956), 264–293.
  • [19] A. Janssen, Charakterisierung stetiger Faltungshalbgruppen durch das Lévy-Maß, Math. Ann. 246 (1979/80), no. 3, 233–240.
  • [20] A. A. Kirillov, Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk 17 (1962), no. 4 (106), 57–110.
  • [21] A. Melin, Parametrix constructions for right invariant differential operators on nilpotent groups, Ann. Global Anal. Geom. 1 (1983), no. 1, 79–130.
  • [22] L. Pukanszky, On the theory of exponential groups, Trans. Amer. Math. Soc. 126 (1967), 487–507.
  • [23] C. Rockland, Hypoellipticity on the Heisenberg group-representation-theoretic criteria, Trans. Amer. Math. Soc. 240 (1978), 1–52.
  • [24] E. Siebert, Absolute continuity, singularity, and supports of Gauss semigroups on a Lie group, Monatsh. Math. 93 (1982), no. 3, 239–253.
  • [25] K. Yosida, Functional analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 123, Springer-Verlag, Berlin, 1980.