Pacific Journal of Mathematics

On a connection between nilpotent groups and oscillatory integrals associated to singularities.

Roger E. Howe

Article information

Source
Pacific J. Math., Volume 73, Number 2 (1977), 329-363.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102810615

Mathematical Reviews number (MathSciNet)
MR0578891

Zentralblatt MATH identifier
0383.22009

Subjects
Primary: 22E45: Representations of Lie and linear algebraic groups over real fields: analytic methods {For the purely algebraic theory, see 20G05}
Secondary: 58C25: Differentiable maps

Citation

Howe, Roger E. On a connection between nilpotent groups and oscillatory integrals associated to singularities. Pacific J. Math. 73 (1977), no. 2, 329--363. https://projecteuclid.org/euclid.pjm/1102810615


Export citation

References

  • [1] M. F. Atiyah, Resolution of singularitiesand divisionof distributions,Comm. Pure and App. Math., 23 (1970).
  • [2] I. N. Bernstein, The analytic continuationof generalized functionswith respect to a parameter, Funk. Anal. PriL, 6 (1972), no. 47, pp. 26-40.
  • [3] I. N. Bernstein and S. I. Gelfand, The functionP is meromorphic,Funk. Anal. PriL, 3 (1967), no. 1, pp. 84-86.
  • [4] L. Corwin and F. Greenleaf, in preparation.
  • [5] J. J. Duistermaat, Fourier Integral Operators, Courant Institute Lecture Notes, N. Y. U., New York, 1973.
  • [6] R. Howe, On representations of discrete, finitely generated, torsion-freenilpotent groups, Pacific J. Math., 73 (1977), 281-305.
  • [7] R. Howe, Topics in harmonicanalysis on solvable algebraic groups, Pacific J. Math., 73 (1977), 383-435.
  • [8] A. A. Kirillov, Unitary representations of nilpotent Lie groups, Usp. Mat. Nauk., 17 (1962), 57-110.
  • [9] B. Kostant, Symplectic spinors, Symp. Math. V, 14 (1974), 139-152.
  • [10] B. Malgrange, Sur les polynomes de I. N. Bernstein,Usp. Mat. Nauk., 29 (1974), no. 4, 178.
  • [11] C. C. Moore and J. Wolfe, Square integrable representations of nilpotent groups, Trans. Amer. Math. Soc, 185 (1974), 445-462.
  • [12] R. Penney, Canonical objects in the Kirillov theory of nilpotent Lie groups, to appear P.A.M.S.
  • [13] N. S. Poulsen, On C-vectorsand intertwiningbilinear forms for representations of Lie groups, J. Functional Analysis, 9 (1972), 87-120.
  • [14] L. Pukanszky, On the theory of exponential groups, T.A.M.S., 126 (1967), 457-507.
  • [15] G. Schiffman, Distributions centrales de type positifsur un groupe de Lie nil- potent, Bull. Soc. Math. France, 96 (1968), 347-355.
  • [16] R. Thom, StructuralStabilityand Morphogenesis.W. A. Benjamin, Reading, Mass., 1975.