Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

Paley-Wiener theorems and surjectivity of invariant differential operators on symmetric spaces and Lie groups


Author: Sigurdur Helgason
Journal: Bull. Amer. Math. Soc. 79 (1973), 129-132
MSC (1970): Primary 22E30, 43A85, 58G99, 35A05
DOI: https://doi.org/10.1090/S0002-9904-1973-13127-1
MathSciNet review: 0312158
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. A. Cerèzo and F. Rouvière, Résolubilité locale d'un opérateur différentiel invariant du premier ordre, Ann. Sci. École Norm. Sup. 4 (1971), 21-30. MR 298702
  • 2. M. Eguchi and K. Okamoto, The Fourier transform of the Schwartz space of a symmetric space, 1972 (preprint). MR 499949
  • 3. L. Ehrenpreis, Solution of some problems of division. I. Division by a polynomial of derivation, Amer. J. Math. 76 (1954), 883-903. MR 16, 834. MR 68123
  • 4. L. Ehrenpreis and F. I. Mautner, Some properties of the Fourier transform on semisimple Lie groups. I, Ann. of Math. (2) 61 (1955), 406-439. MR 16, 1017. MR 69311
  • 5. R. Gangolli, On the Plancherel formula and the Paley-Wiener theorem for spherical functions on semisimple Lie groups, Ann. of Math. (2) 93 (1971), 150-165. MR 289724
  • 6. Harish-Chandra, Spherical functions on a semisimple Lie group. I, II, Amer. J. Math. 80 (1958), 241-310, 553-613. MR 20 #925; MR 21 #92. MR 94407
  • 7. Harish-Chandra, Differential equations and semisimple Lie groups, 1960 (unpublished).
  • 8. Harish-Chandra, Invariant eigendistributions on a semisimple Lie group, Trans. Amer. Math. Soc. 119 (1965), 457-508. MR 31 #4862d. MR 180631
  • 9. Harish-Chandra, Discrete series for semisimple Lie groups. II. Explicit determination of the characters, Acta Math. 116 (1966), 1-111. MR 36 #2745. MR 219666
  • 10. S. Helgason, Duality and Radon transform for symmetric spaces, Amer. J. Math. 85 (1963), 667-692. MR 28 #1632. MR 158409
  • 11. S. Helgason, Fundamental solutions of invariant differential operators on symmetric spaces, Amer. J. Math. 86 (1964), 565-601. MR 29 #2323. MR 165032
  • 12. S. Helgason, The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds, Acta Math. 113 (1965), 153-180. MR 30 #2530. MR 172311
  • 13. S. Helgason, Radon-Fourier transforms on symmetric spaces and related group representations, Bull. Amer. Math. Soc. 71 (1965), 757-763. MR 31 #3543. MR 179295
  • 14. S. Helgason, An analog of the Paley-Wiener theorem for the Fourier transform on certain symmetric spaces, Math. Ann. 165 (1966), 297-308. MR 36 #6545. MR 223497
  • 15. S. Helgason, A duality for symmetric spaces with applications to group representations, Advances in Math. 5 (1970), 1-154. MR 41 #8587. MR 263988
  • 16. L. Hörmander, On the division of distributions by polynomials, Ark. Mat. 3 (1958), 555-568. MR 23 #A2044. MR 124734
  • 17. P. D. Lax and R. S. Phillips, The Paley-Wiener theorem for the Radon transform, Comm. Pure Appl. Math. 23 (1970), 409-424; Correction, ibid. 24 (1971), 279-288. MR 42 #8189; #8190. MR 273309
  • 18. S. Lojasiewicz, Sur le problème de la division, Studia Math. 18 (1959), 87-136. MR 21 #5893. MR 107168
  • 19. D. Ludwig, The Radon transform on euclidean space, Comm. Pure Appl. Math. 19 (1966), 49-81. MR 32 #8064. MR 190652
  • 20. B. Malgrange, Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution, Ann. Inst. Fourier (Grenoble) 6 (1955/56), 271-355. MR 19, 280. MR 86990
  • 21. M. Raïs, Solutions élémentaires des opérateurs différentiels bi-invariants sur un groupe de Lie nilpotent, C. R. Acad. Sci. Paris 273 (1971), 495-498. MR 289720
  • 22. G. Warner, Harmonic analysis on semisimple Lie groups, Springer-Verlag, Berlin and New York (to appear).

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1970): 22E30, 43A85, 58G99, 35A05

Retrieve articles in all journals with MSC (1970): 22E30, 43A85, 58G99, 35A05


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1973-13127-1

American Mathematical Society