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)

 
 

 

Analytic and entire vectors for representations of Lie groups


Author: Roe W. Goodman
Journal: Trans. Amer. Math. Soc. 143 (1969), 55-76
MSC: Primary 22.60
DOI: https://doi.org/10.1090/S0002-9947-1969-0248285-6
MathSciNet review: 0248285
Full-text PDF Free Access

References | Similar Articles | Additional Information

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

  • [1] L. Bers, F. John and M. Schechter, ``Partial differential equations'' in Lectures in applied mathematics, Vol. III, Interscience, New York, 1964. MR 0163043 (29:346)
  • [2] R. J. Blattner, On induced representations, Amer. J. Math. 83 (1961), 79-98. MR 0125456 (23:A2757)
  • [3] F. Browder, Real analytic functions on product spaces and separate analyticity, Canad. J. Math. 13 (1961), 650-656. MR 0132395 (24:A2240)
  • [4] F. Bruhat, Sur les représentations induites des groupes de Lie, Bull. Soc. Math. France 84 (1956), 97-205. MR 0084713 (18:907i)
  • [5] P. Cartier, Représentations des groupes de Lie, Séminaire Bourbaki #96 (1954); reprint, Benjamin, New York, 1967.
  • [6] N. Dunford and J. Schwartz, Linear operators, Vol. II, Interscience, New York, 1963. MR 0188745 (32:6181)
  • [7] R. Godement, A theory of spherical functions. I, Trans. Amer. Math. Soc. 73 (1952), 496-556. MR 0052444 (14:620c)
  • [8] I. Gelfand and M. Naimark, Unitary representations of the group of linear transformations of the straight line, Dokl. Akad. Nauk SSSR 55 (1947), 567-570. MR 0020559 (8:563c)
  • [9] R. Goodman, Analytic domination by fractional powers of a positive operator, J. Functional Analysis 3 (1969), 246-264. MR 0239444 (39:801)
  • [10] S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962. MR 0145455 (26:2986)
  • [11] E. Hille, Contributions to the theory of Hermitian series. II. The representation problem, Trans. Amer. Math. Soc. 47 (1940), 80-94. MR 0000871 (1:142a)
  • [12] G. Hochschild, The structure of Lie groups, Holden-Day, San Francisco, Calif., 1965. MR 0207883 (34:7696)
  • [13] Y. Katznelson, An introduction to harmonic analysis, Wiley, New York, 1968. MR 0248482 (40:1734)
  • [14] R. Kunze and I. E. Segal, Integrals and operators, McGraw-Hill, New York, 1968. MR 0217244 (36:335)
  • [15] N. N. Lebedev, Sur une formule d'inversion, Dokl. Akad. Nauk SSSR 52 (1946), 655-658.
  • [16] G. W. Mackey, Induced representations of locally compact groups. I, Ann. of Math. 55 (1952), 101-139. MR 0044536 (13:434a)
  • [17] W. Magnus, F. Oberhettinger and R. P. Soni, Formulas and theorems for the special functions of mathematical physics, Springer, New York, 1966. MR 0232968 (38:1291)
  • [18] R. T. Moore, Measurable, continuous, and smooth vectors for semigroups and group representations, Mem. Amer. Math. Soc. No. 78, 1968. MR 0229091 (37:4669)
  • [19] M. A. Naimark, Linear representations of the Lorentz groups, Macmillan, New York, 1964. MR 0170977 (30:1211)
  • [20] E. Nelson, Analytic vectors, Ann. of Math. 70 (1959), 572-615. MR 0107176 (21:5901)
  • [21] E. Nelson and W. F. Stinespring, Representation of elliptic operators in an enveloping algebra, Amer. J. Math. 81 (1959), 547-560. MR 0110024 (22:907)
  • [22] R. E. A. C. Paley and N. Wiener, Fourier transforms in the complex domain, Amer. Math. Soc. Colloq. Publ., Vol. 19, Amer. Math. Soc., Providence, R. I., 1934; reprinted 1967. MR 1451142 (98a:01023)
  • [23] G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis. I, Springer, Berlin, 1954.
  • [24] L. Pukanszky, Leçons sur les représentations des groupes, Dunod, Paris, 1967. MR 0217220 (36:311)
  • [25] I. E. Segal and J. von Neumann, A theorem on unitary representations of semi-simple Lie groups, Ann. of Math. 52 (1950), 509-517. MR 0037309 (12:242a)
  • [26] T. Sherman, A weight theory for unitary representations, Canad. J. Math. 18 (1966), 159-168. MR 0193189 (33:1410)
  • [27] I. M. Singer, Uniformly continuous representations of Lie groups, Ann. of Math. 56 (1952), 242-247. MR 0049201 (14:135a)
  • [28] E. M. Stein, Analytic continuation of group representations, Lectures, Yale University, 1967. MR 0466418 (57:6298)
  • [29] E. C. Titchmarsh, Eigenfunction expansions, Part I, 2nd ed., Oxford Univ. Press, Oxford, 1962. MR 0176151 (31:426)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22.60

Retrieve articles in all journals with MSC: 22.60


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1969-0248285-6
Article copyright: © Copyright 1969 American Mathematical Society

American Mathematical Society