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Global solvability on compact Heisenberg manifolds
Author:
Leonard F. Richardson
Journal:
Trans. Amer. Math. Soc. 273 (1982), 309-317
MSC:
Primary 22E25; Secondary 35F99, 58G05
MathSciNet review:
664044
Full-text PDF Free Access
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Abstract: We apply the methods of primary and irreducible Fourier series on compact nilmanifolds to determine the ranges of all first order invariant operators on the compact Heisenberg manifolds. We show that the sums of primary solutions behave better on these manifolds than on any multidimensional torus.
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general compact nilmanifold, Amer. J. Math. 93
(1971), 173–190. MR 0284546
(44 #1771)
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Leonard
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- [1]
- L. Auslander and J. Brezin, Uniform distribution in solvmanifolds, Advances in Math. 7 (1971), 111-144. MR 0301137 (46:295)
- [2]
- L. Auslander, L. Green and F. Hahn, Flows on homogeneous spaces, Ann. of Math. Studies, no. 53, Princeton Univ. Press, Princeton, N. J., 1963.
- [3]
- L. Auslander and R. Tolimieri, Abelian harmonic analysis, theta functions and function algebras on a nilmanifold, Lecture Notes in Math., vol. 436, Springer-Verlag, Berlin and New York, 1975. MR 0414785 (54:2877)
- [4]
- L. Corwin and F. Greenleaf, Integral formulas with distribution kernels for irreducible projections in
 of a nilmanifold, J. Functional Analysis 23 (1976), 255-284. MR 0460535 (57:528)
- [5]
- L. Corwin, F. Greenleaf, and R. Penney, A canonical formula for the distribution kernels of primary projections in
 of a nilmanifold, Comm. Pure Appl. Math. 30 (1977), 355-372. MR 0430157 (55:3164)
- [6]
- J. Dadok and M. Taylor, Local solvability of constant coefficient partial differential equations as a small divisor problem, preprint. MR 603601 (82h:35014)
- [7]
- H. Dym and H. McKean, Fourier series and integrals, Academic Press, New York, 1972. MR 0442564 (56:945)
- [8]
- G. Hardy and E. Wright, An introduction to the theory of numbers, 3rd ed., Oxford Univ. Press, New York and London, 1954. MR 0067125 (16:673c)
- [9]
- B. Helffer, Hypoellipticite pour des operateurs differentiels sur des groupes de Lie nilpotents, preprint. MR 660651 (83h:22015)
- [10]
- I. Niven, Irrational numbers, Carus Monograph No. 11, Math. Assoc. Amer., New York, 1956. MR 0080123 (18:195c)
- [11]
- L. Richardson, Decomposition of the
 -space of a general compact nilmanifold, Amer. J. Math. 93 (1971), 173-190. MR 0284546 (44:1771)
- [12]
- -, A class of idempotent measures on compact nilmanifolds, Acta Math. 135 ( 1975), 129-154. MR 0486324 (58:6080)
- [13]
- G. Warner, Harmonic analysis on semi-simple Lie groups. I, Springer-Verlag, Berlin and New York, 1972. MR 0498999 (58:16979)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1982-0664044-0
PII:
S 0002-9947(1982)0664044-0
Article copyright:
© Copyright 1982 American Mathematical Society
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