Analytic and entire vectors for representations of Lie groups

Analytic and entire vectors for representations of Lie groups
HTML articles powered by AMS MathViewer

Trans. Amer. Math. Soc. 143 (1969), 55-76

DOI: https://doi.org/10.1090/S0002-9947-1969-0248285-6

PDF | Request permission

References

Lipman Bers, Fritz John, and Martin Schechter, Partial differential equations, Lectures in Applied Mathematics, Vol. III, Interscience Publishers, a division of John Wiley & Sons, Inc., New York-London-Sydney, 1964. With special lectures by Lars Garding and A. N. Milgram. MR 0163043
Robert J. Blattner, On induced representations, Amer. J. Math. 83 (1961), 79–98. MR 125456, DOI 10.2307/2372722
Felix E. Browder, Real analytic functions on product spaces and separate analyticity, Canadian J. Math. 13 (1961), 650–656. MR 132395, DOI 10.4153/CJM-1961-054-1
François Bruhat, Sur les représentations induites des groupes de Lie, Bull. Soc. Math. France 84 (1956), 97–205 (French). MR 84713

Représentations des groupes de Lie

Nelson Dunford and Jacob T. Schwartz, Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space, Interscience Publishers John Wiley & Sons, New York-London, 1963. With the assistance of William G. Bade and Robert G. Bartle. MR 0188745
Roger Godement, A theory of spherical functions. I, Trans. Amer. Math. Soc. 73 (1952), 496–556. MR 52444, DOI 10.1090/S0002-9947-1952-0052444-2
I. Gelfand and M. Neumark, Unitary representations of the group of linear transformations of the straight line, C. R. (Doklady) Acad. Sci. URSS (N.S.) 55 (1947), 567–570. MR 0020559
Roe Goodman, Analytic domination by fractional powers of a positive operator, J. Functional Analysis 3 (1969), 246–264. MR 0239444, DOI 10.1016/0022-1236(69)90042-1
Sigurđur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962. MR 0145455
Einar Hille, Contributions to the theory of Hermitian series. II. The representation problem, Trans. Amer. Math. Soc. 47 (1940), 80–94. MR 871, DOI 10.1090/S0002-9947-1940-0000871-3
G. Hochschild, The structure of Lie groups, Holden-Day, Inc., San Francisco-London-Amsterdam, 1965. MR 0207883
Yitzhak Katznelson, An introduction to harmonic analysis, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0248482
Irving E. Segal and Ray A. Kunze, Integrals and operators, McGraw-Hill Book Co., New York-Toronto-London, 1968. MR 0217244

Sur une formule d’inversion

52

George W. Mackey, Induced representations of locally compact groups. I, Ann. of Math. (2) 55 (1952), 101–139. MR 44536, DOI 10.2307/1969423
Wilhelm Magnus, Fritz Oberhettinger, and Raj Pal Soni, Formulas and theorems for the special functions of mathematical physics, Third enlarged edition, Die Grundlehren der mathematischen Wissenschaften, Band 52, Springer-Verlag New York, Inc., New York, 1966. MR 0232968
Robert T. Moore, Measurable, continuous and smooth vectors for semi-groups and group representations, Memoirs of the American Mathematical Society, No. 78, American Mathematical Society, Providence, R.I., 1968. MR 0229091
M. A. Naimark, Linear representations of the Lorentz group, A Pergamon Press Book, The Macmillan Company, New York, 1964. Translated by Ann Swinfen and O. J. Marstrand; translation edited by H. K. Farahat. MR 0170977
Edward Nelson, Analytic vectors, Ann. of Math. (2) 70 (1959), 572–615. MR 107176, DOI 10.2307/1970331
Edward Nelson and W. Forrest Stinespring, Representation of elliptic operators in an enveloping algebra, Amer. J. Math. 81 (1959), 547–560. MR 110024, DOI 10.2307/2372913
Raymond E. A. C. Paley and Norbert Wiener, Fourier transforms in the complex domain, American Mathematical Society Colloquium Publications, vol. 19, American Mathematical Society, Providence, RI, 1987. Reprint of the 1934 original. MR 1451142, DOI 10.1090/coll/019

Aufgaben und Lehrsätze aus der Analysis

L. Pukánszky, Leçons sur les représentations des groupes, Monographies de la Société Mathématique de France, No. 2, Dunod, Paris, 1967 (French). MR 0217220
I. E. Segal and John von Neumann, A theorem on unitary representations of semisimple Lie groups, Ann. of Math. (2) 52 (1950), 509–517. MR 37309, DOI 10.2307/1969429
Thomas Sherman, A weight theory for unitary representations, Canadian J. Math. 18 (1966), 159–168. MR 193189, DOI 10.4153/CJM-1966-020-0
I. M. Singer, Uniformly continuous representations of Lie groups, Ann. of Math. (2) 56 (1952), 242–247. MR 49201, DOI 10.2307/1969797
Elias M. Stein, Analytic continuation of group representations, Yale Mathematical Monographs, vol. 2, Yale University Press, New Haven, Conn.-London, 1971. A James K. Whittemore Lecture in Mathematics given at Yale University, 1967. MR 0466418
E. C. Titchmarsh, Eigenfunction expansions associated with second-order differential equations. Part I, 2nd ed., Clarendon Press, Oxford, 1962. MR 0176151