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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
MathSciNet review:
0312158
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Similar Articles |
Additional Information
- 1.
A.
Cerezo and F.
Rouvière, Résolubilité locale d’un
opérateur différentiel invariant du premier ordre, Ann.
Sci. École Norm. Sup. (4) 4 (1971), 21–30
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0298702 (45 #7751)
- 2.
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(16,834a)
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Gangolli, On the Plancherel formula and the Paley-Wiener theorem
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Invariant eigendistributions on a
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457–508. MR 0180631
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Discrete series for semisimple Lie groups. II. Explicit determination
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S.
Helgason, Duality and Radon transform for symmetric spaces,
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- 11.
S.
Helgason, Fundamental solutions of invariant differential operators
on symmetric spaces, Amer. J. Math. 86 (1964),
565–601. MR 0165032
(29 #2323)
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Sigurđur
Helgason, The Radon transform on Euclidean spaces, compact
two-point homogeneous spaces and Grassmann manifolds, Acta Math.
113 (1965), 153–180. MR 0172311
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S.
Helgason, Radon-Fourier transforms on symmetric
spaces and related group representations, Bull.
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(1965), 757–763. MR 0179295
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Sigurđur
Helgason, An analogue of the Paley-Wiener theorem for the Fourier
transform on certain symmetric spaces, Math. Ann. 165
(1966), 297–308. MR 0223497
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Helgason, A duality for symmetric spaces with applications to group
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(41 #8587)
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Hörmander, On the division of distributions by
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(23 #A2044)
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S. Phillips, The Paley-Wiener theorem for the Radon transform,
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Łojasiewicz, Sur le problème de la division,
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(21 #5893)
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Donald
Ludwig, The Radon transform on euclidean space, Comm. Pure
Appl. Math. 19 (1966), 49–81. MR 0190652
(32 #8064)
- 20.
Bernard
Malgrange, Existence et approximation des solutions des
équations aux dérivées partielles et des
équations de convolution, Ann. Inst. Fourier, Grenoble
6 (1955–1956), 271–355 (French). MR 0086990
(19,280a)
- 21.
Mustapha
Raïs, Solutions élémentaires des
opérateurs différentiels bi-inbariants sur un groupe de Lie
nilpotent, C. R. Acad. Sci. Paris Sér. A-B 273
(1971), A495–A498 (French). MR 0289720
(44 #6908)
- 22.
G. Warner, Harmonic analysis on semisimple Lie groups, Springer-Verlag, Berlin and New York (to appear).
- 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).
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9904-1973-13127-1
PII:
S 0002-9904(1973)13127-1
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