Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Some properties of the Fourier transform on semi-simple Lie groups. II


Authors: L. Ehrenpreis and F. I. Mautner
Journal: Trans. Amer. Math. Soc. 84 (1957), 1-55
MSC: Primary 17.0X
DOI: https://doi.org/10.1090/S0002-9947-1957-0083683-7
MathSciNet review: 0083683
Full-text PDF Free Access

References | Similar Articles | Additional Information

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

  • [V] Bargmann 1. Unitary representations of the Lorentz group, Ann. of Math. vol. 48 (1947) pp. 568-640. MR 0021942 (9:133a)
  • [N] Bourbaki 1. XV, Livre V. Espaces vectoriels topologiques, Paris, Hermann, 1953. MR 0054161 (14:880b)
  • [2] XIII, Livre 6. Integration, Chapter III. Paris, Hermann, 1953.
  • [L] Delsarte 1. Sur une extension de la formule de Taylor, J. Math. Pures Appl. vol. 17 (1938).
  • [J] Dieudonné and L. Schwartz 1. La dualité dans les espaces $ (F)$ et $ (LF)$. Ann. Institut Fourier (Grenoble) vol. 1, (1950) pp. 61-101. MR 0038553 (12:417d)
  • [L] Ehrenpreis 1. Theory of distributions for locally compact spaces, Memoirs of the American Mathematical Society, no. 21, 1956. MR 0098317 (20:4778)
  • [2] Some properties of distributions on Lie groups (to appear in Pacific Journal of Mathematics).
  • [3] Solutions of some problems of division I, Amer. J. Math. vol. 76 (1954) pp. 883-903. MR 0068123 (16:834a)
  • [4] Analytic functions and the Fourier transform of distributions I, Ann. of Math. vol. 63 (1956) pp. 129-159. MR 0076297 (17:876g)
  • [5] Mean periodic functions I, Amer. J. Math. vol. 78 (1955) pp. 293-328.
  • [L] Ehrenpreis and F. I. Mautner 1. Some properties of the Fourier transform on semi-simple Lie groups. I, Ann. of Math. vol. 61 (1955) pp. 406-439. MR 0069311 (16:1017b)
  • [A] Grothendieck 1. Sur les espaces $ (F)$ et $ (DF)$, Summa Brasiliensis Mathematicae vol. 3 (1954) pp. 57-121. MR 0075542 (17:765b)
  • 1. Harish-Chandra 1. Plancherel formula for the real $ 2 \times 2$ unimodular group, Proc. Nat. Acad. Sci. U.S.A. vol. 38 (1952) pp. 337-342. MR 0047055 (13:820h)
  • [F] I. Mautner 1. Unitary representations of locally compact groups I, Ann. of Math. vol. 51 (1950) pp. 1-25. MR 0032650 (11:324d)
  • [2] Unitary representations of locally compact groups II, Ann. of Math. 52 (1950) pp. 528-556. MR 0036763 (12:157d)
  • [3] Fourier analysis and symmetric spaces, Proc. Nat. Acad. Sci. U.S.A. vol. 37 (1951) pp. 529-533. MR 0044537 (13:434b)
  • [4] Note on the Fourier inversion formula on groups, Trans. Amer. Math. Soc. vol. 78 (1955) pp. 371-384. MR 0067230 (16:692d)
  • [5] Induced representations, Amer. J. Math. vol. 74 (1952) pp. 737-758. MR 0049199 (14:134d)
  • [R] E. A. C. Paley and N. Wiener 1. Fourier transform in the complex domain, Amer. Math. Soc. Colloquium Publications, vol. 19, 1934. MR 1451142 (98a:01023)
  • [A] Powsner 1. On differential equations of the Sturm-Liouville type on a half-axis, Rec. Math. (Mat. Sbornik) N.S. vol. 23 (1948) pp. 3-52. MR 0027403 (10:299h)
  • [L] Schwartz 1. Etude des sommes d'exponentielles réelles, Paris, Hermann, 1943.
  • [2] Approximation d'une function quelqonque per des sommes d'exponentielles imaginaires, Ann. Fac. Sci. Univ. Toulouse (4) vol. 6, (1942) pp. 111-174.
  • [3] Théorie générale des fonctions moyenne-periodique, Ann. of Math. vol. 48 (1947), pp. 857-929. MR 0023948 (9:428c)
  • [4] Theorie des distributions, vols. I and II, Paris, Hermann, 1950-1951.
  • [5] Analyse et synthèse harmonique dans les espaces de distributions, Canadian Journal of Mathematics vol. 3 (1951) pp. 503-512. MR 0044754 (13:473c)
  • [6] Théorie des noyaux, Proceedings of the International Congress of Mathematicians, 1950, vol. 1, pp. 220-230.
  • [E] C. Titchmarsh 1. The theory of functions, Oxford University Press, 1932. MR 0197687 (33:5850)
  • [2] Theory of Fourier integral, Oxford University Press, 1937.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 17.0X

Retrieve articles in all journals with MSC: 17.0X


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1957-0083683-7
Article copyright: © Copyright 1957 American Mathematical Society

American Mathematical Society