Analyticity of relative fundamental solutions and projections for left invariant operators on the Heisenberg group

Linda Preiss Rothschild; David S. Tartakoff

Annales scientifiques de l'École Normale Supérieure (1982)

  • Volume: 15, Issue: 3, page 419-440
  • ISSN: 0012-9593

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Rothschild, Linda Preiss, and Tartakoff, David S.. "Analyticity of relative fundamental solutions and projections for left invariant operators on the Heisenberg group." Annales scientifiques de l'École Normale Supérieure 15.3 (1982): 419-440. <http://eudml.org/doc/82101>.

@article{Rothschild1982,
author = {Rothschild, Linda Preiss, Tartakoff, David S.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {analyticity; relative fundamental solutions; left invariant operators; Heisenberg group; transversally elliptic operator; existence},
language = {eng},
number = {3},
pages = {419-440},
publisher = {Elsevier},
title = {Analyticity of relative fundamental solutions and projections for left invariant operators on the Heisenberg group},
url = {http://eudml.org/doc/82101},
volume = {15},
year = {1982},
}

TY - JOUR
AU - Rothschild, Linda Preiss
AU - Tartakoff, David S.
TI - Analyticity of relative fundamental solutions and projections for left invariant operators on the Heisenberg group
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1982
PB - Elsevier
VL - 15
IS - 3
SP - 419
EP - 440
LA - eng
KW - analyticity; relative fundamental solutions; left invariant operators; Heisenberg group; transversally elliptic operator; existence
UR - http://eudml.org/doc/82101
ER -

References

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  1. [1] R. BEALS and P. GREINER, In preparation. 
  2. [2] D. GELLER, Fourier Analysis on the Heisenberg Group II: Local Solvability and Homogeneous distributions (Comm. in P.D.E., Vol. 5, No 5, 1980, pp. 475-560). Zbl0488.22020MR81i:35004
  3. [3] R. GOODMAN, Nilpotent Lie groups: Structure and Applications to Analysis (Lecture Notes in Math., Vol. 562, Springer-Verlag, 1976). Zbl0347.22001MR56 #537
  4. [4] P. GREINER, J. J. KOHN and E. M. STEIN, Necessary and Sufficient Conditions for Local Solvability of the Lewy Equation (Proc. Natl. Acad. Sc. U.S.A., Vol. 72, No. 9, 1975, pp. 3287-3289). Zbl0308.35017MR52 #1043
  5. [5] V. V. GRUSIN, On a Class of Hypoelliptic Operators (Math. Sb., Vol. 83, 185, 1970, No. 3, pp. 456-473); Math. U.S.S.R. Sb., Vol. 12, No. 3, 1972, pp. 458-476. Zbl0252.35057MR43 #5158
  6. [6] B. HELFFER and J. NOURRIGAT, Hypoellipticité pour des groupes nilpotents de rang 3 (Comm. in P.D.E., Vol. 3, 1978, pp. 643-743). Zbl0385.35015MR81d:35016
  7. [7] L. HORMANDER, Linear Partial Differential Operators, New York, 1969. Zbl0175.39201MR40 #1687
  8. [8] A. A. KIRILLOV, Unitary Representations of Nilpotent Lie groups, (Usp. Math. Nauk 17, 1962, pp. 57-110, Russian Math. Surveys, Vol. 17, 1962, pp. 53-104). Zbl0106.25001MR25 #5396
  9. [9] G. LION, Hypoellipticité et résolubitité d'opérateurs différentiels sur des groupes nilpotents de rang 2 (C. R. Acad. Sc., Paris, T. 290, 1980, pp. 271-274). Zbl0434.35026MR81a:58045
  10. [10] A. MELIN, Parametrix Constructions for Some Classes of Right-Invariant Differential Operators on the Heisenberg Group, (to appear). Zbl0486.35007
  11. [11] G. MÉTIVIER, Hypoellipticité analytique sur des groupes nilpotents de rang 2 (Duke Math. J., Vol. 47, 1980, pp. 195-221). Zbl0433.35015MR81i:35037
  12. [12] E. NELSON, Analytic Vectors (Ann. of Math., Vol. 70, No. 3, 1959, pp. 572-615). Zbl0091.10704MR21 #5901
  13. [13] L. PUKANSZKY, Leçons sur les représentations des groupes; Paris, 1967. Zbl0152.01201MR36 #311
  14. [14] C. ROCKLAND, Hypoellipticity on the Heisenberg Group, (Trans. Amer. Math. Soc., Vol. 240, No. 517, 1978, pp. 1-52). Zbl0326.22007MR58 #6071
  15. [15] L. P. ROTHSCHILD and D. S. TARTAKOFF, Inversion of Analytic Matrices and Local Solvability of Some Invariant Differential Operators on Nilpotent Lie Groups (Comm. in P.D.E. 6 (6) 1981, pp. 625-650.) Zbl0477.58032MR84g:22026
  16. [16] D. S. TARTAKOFF, The Local Real Analyticity of Solutions to ☐b and the ∂-Neumann Problem (Acta Mathematica, Vol. 145, 1980, pp. 177-204). Zbl0456.35019MR81k:35033
  17. [17] D. S. TARTAKOFF, Local Analytic Hypoellipticity for ☐b on Non-Degenerate Cauchy-Riemann Manifolds (Proc. Nat. Acad. Sc., U.S.A., Vol. 75, 1978, pp. 3027-3028). Zbl0384.35020MR80g:58045
  18. [18] F. TRÈVES, Analytic Hypo-Ellipticy of a Class of Pseudo-Differential Operators with Double Characteristics and Applications to the ∂-Neumann Problem (Comm. in P.D.E., Vol. 3, 1978, pp. 475-642). Zbl0384.35055MR58 #11867

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