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Functions on locally compact groups


Author: George W. Mackey
Journal: Bull. Amer. Math. Soc. 56 (1950), 385-412
DOI: https://doi.org/10.1090/S0002-9904-1950-09403-8
MathSciNet review: 0039729
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  • 1. W. Ambrose, Spectral resolution of groups of unitary operators, Duke Math. J. vol. 11 (1944) pp. 589-595. MR 11172
  • 2. W. Ambrose, The L, Trans. Amer. Math. Soc. vol. 65 (1949) pp. 27-48. MR 28322
  • 3. V. Bargmann, Irreducible unitary representations of the Lorentz group, Ann. of Math. vol. 48 (1947) pp. 568-640. MR 21942
  • 4. S. Bochner, Beiträge zur Theorie der fastperiodischen Funktionen, Math. Ann. vol. 96 (1927) pp. 119-147. MR 1512308
  • 5. S. Bochner, Vorlesungen über Fouriersche Integrale, Leipzig, Akad. Verlagsges., 1932.
  • 6. S. Bochner and J. von Neumann, Almost periodic functions in groups, Trans. Amer. Math. Soc. vol. 37 (1935) pp. 21-50. MR 1501777
  • 7. H. Cartan and R. Godement, Théorie de la dualité et analyse harmonique dans les groupes abéliens localement compact, Ann. École Norm. vol. 64 (1947) pp. 79-99. MR 23241
  • 8. J. Dixmier, Les anneaux d'operateurs de classe finie, Ann. École Norm. (3) vol. 66 (1950) pp. 209-261. MR 32940
  • 9. H. Freudenthal, Topologische Gruppen mit genugend vielen fastperiodischen Funktionen, Ann. of Math. vol. 37 (1936) pp. 57-77. MR 1503269
  • 10. I. Gelfand, Normierte Ringe, Rec. Math. (Mat. Sbornik) N. S. vol. 9 (1941) pp. 3-24. MR 4726
  • 11. I. Gelfand, Über absolut konvergente trigonometrische Reihen und Integrale, Rec. Math. (Mat. Sbornik) N. S. vol. 9 (1941) pp. 51-66. MR 4727
  • 12. I. Gelfand and M. Neumark, Unitary representations of the group of linear transformations of the straight line, C. R. (Doklady) Acad. Sci. URSS. vol. 55 (1947) pp. 567-570. MR 20559
  • 13. I. Gelfand and M. Neumark, The principal series of irreducible representations of the complex unimodular group, C. R. (Doklady) Acad. Sci. URSS. vol. 56 (1947) pp. 3-4. MR 20998
  • 14. I. Gelfand and M. Neumark, Supplementary and degenerate series of representations of the complex unimodular group, C. R. (Doklady) Acad. Sci. URSS. vol. 58 (1947) pp. 1577-1580. MR 23247
  • 15. I. Gelfand and M. Neumark, Unitary representations of the Lorentz group, Izvestiya Akademii Nauk SSSR. Ser. Mat. vol. 11 (1947) pp. 411-504. MR 24440
  • 16. I. Gelfand and M. Neumark, Unitary representations of semi simple Lie groups I, Rec. Math. (Mat. Sbornik) N. S. vol. 21 (1947) pp. 405-434. MR 23246
  • 17. I. Gelfand and M. Neumark, On the connection between the representations of a complex simple Lie group and those of its maximal compact subgroups, Doklady Akad. Nauk SSSR. vol. 63 (1948) pp. 225-228. MR 27279
  • 18. I. Gelfand and M. Neumark, The analogue of Plancherel's formula for the complex unimodular group, Doklady Akad. Nauk SSSR. vol. 63 (1948) pp. 609-612. MR 28324
  • 19. I. Gelfand and M. Neumark, Normed rings with involution and their representations, Izvestiya Akademii Nauk SSSR. Ser. Mat. vol. 12 (1948) pp. 445-480. MR 26763
  • 20. I. Gelfand and D. Raikov, On the theory of character of commutative topological groups, C. R. (Doklady) Acad. Sci. URSS. vol. 28 (1940) pp. 195-198. MR 3423
  • 21. I. Gelfand and M. Neumark, Irreducible unitary representations of locally bicompact groups, Rec. Math. (Mat. Sbornik) N. S. vol. 13 (1943) pp. 301-316. MR 11308
  • 22. I. Gelfand, D. Raikov, and G. Silov, Commutative normed rings, Uspehi Matematičeskih Nauk. N. S. vol. 2 (1946) pp. 48-146. MR 27130
  • 23. R. Godement, Sur une généralisation d'un théorème de Stone, C. R. Acad. Sci. Paris vol. 218 (1944) pp. 901-903. MR 14589
  • 24. R. Godement, Analyse harmonique dans les groupes centraux I. Fonctions centrales et caractères, C. R. Acad. Sci. Paris vol. 225 (1947) pp. 19-21. MR 21000
  • 25. R. Godement, Analyse harmonique dans les groupes centraux II. Formule d'inversion de Fourier, C. R. Acad. Sci. Paris vol. 225 (1947) pp. 221-223. MR 21946
  • 26. R. Godement, Théorèmes taubériens et théorie spectrale, Ann. École Norm. vol. 64 (1947) pp. 119-138. MR 23242
  • 27. R. Godement, Les fonctions de type positif et la théorie des groupes, Trans. Amer. Math. Soc. vol. 63 (1948) pp. 1-84. MR 23243
  • 28. R. Godement, Sur la transformation de Fourier dans les groupes discrets, C. R. Acad. Sci. Paris vol. 228 (1949) pp. 627-628. MR 28323
  • 29. R. Godement, Théorie générale des sommes continues d'espaces de Banach, C. R. Acad. Sci. Paris vol. 228 (1949) pp. 1321-1323. MR 29102
  • 30. R. Godement, Sur la théorie des caractères. I. Definition et classification des caractères, C. R. Acad. Sci. Paris vol. 229 (1949) pp. 967-969. MR 32651
  • 31. R. Godement, Sur la théorie des caractères. II. Mesures et groupes de classe finie, C. R. Acad. Sci. Paris vol. 229 (1949) pp. 1050-1051. MR 32652
  • 32. R. Godement, Sur la théorie des caractères. III. Un exemple de mesure-caractère de classe(I), C. R. Acad. Sci. Paris vol. 229 (1949) pp. 1107-1109. MR 32653
  • 33. R. Godement, Mémoire sur la théorie des caractères dans les groupes localement compacts unimodulaire, to be published.
  • 34. A. Haar, Der Massbegriff in der Theorie der kontinuierlichen Gruppen, Ann. of Math. vol. 34 (1933) pp. 147-169. MR 1503103
  • 35. Harish-Chandra, Infinite irreducible representations of the Lorentz group, Proc. Royal Soc. London Ser. A vol. 189 (1947) pp. 372-401. MR 21941
  • 36. P. R. Halmos, Measure theory, New York, 1950. MR 33869
  • 37. A. Hurevitsch, Unitary representations in Hilbert space of a compact topological group, Rec. Math. (Mat. Sbornik) N. S. vol. 13 (1943) pp. 79-86. MR 11309
  • 38. S. Kakutani, On the uniqueness of Haar's measure, Proc. Imp. Acad. Tokyo vol. 14 (1938) pp. 27-31.
  • 39. E. R. van Kampen, Locally bicompact groups and their character groups, Ann. of Math. vol. 36 (1935) pp. 448-463.
  • 40. E. R. van Kampen, Almost periodic functions and compact groups, Ann. of Math. vol. 37 (1936) pp. 78-91. MR 1503270
  • 41. I. Kaplansky, Primary ideals in group algebras, Proc. Nat. Acad. Sci. U.S.A. vol. 35 (1949) pp. 133-136. MR 28318
  • 42. G. Köthe, Abstracte Theorie nichtkommutativer Ringe mit einer Anwendung auf die Darstellungstheorie kontinuierlicher Gruppen, Math. Ann. vol. 103 (1930) pp. 545-572. MR 1512637
  • 43. M. Krein, Sur une généralisation du théorème de Plancherel au cas des integrales de Fourier sur les groupes topologiques commutatifs. C. R. (Doklady) Acad. Sci. URSS. vol. 30 (1941) pp. 484-488. MR 4087
  • 44. M. Krein and D. Milman, On extreme points of regular convex sets, Studia Mathematica vol. 9 (1940) pp. 133-138. MR 4990
  • 45. B. Lewitan, On the theory of unitary representations of locally compact groups, Rec. Math. (Mat. Sbornik) N. S. vol. 19 (1946) pp. 407-427. MR 20999
  • 46. G. W. Mackey, The Laplace transform for locally compact Abelian groups, Proc. Nat. Acad. Sci. U.S.A. vol. 34 (1948) pp. 156-162. MR 24446
  • 47. G. W. Mackey, Imprimitivity for representations of locally compact groups, Proc. Nat. Acad. Sci. U.S.A. vol. 35 (1949) pp. 537-545. MR 31489
  • 48. F. I. Mautner, The completeness of the irreducible unitary representations of a locally compact group, Proc. Nat. Acad. Sci. U.S.A. vol. 34 (1948) pp. 52-54. MR 23245
  • 49. F. I. Mautner, Unitary representations of locally compact groups I, Ann. of Math. vol. 51 (1950) pp. 1-25. MR 32650
  • 50. F. I. Mautner, Completeness relations on locally compact groups, Bull. Amer. Math. Soc. Abstract 55-1-46.
  • 51. F. I. Mautner, Unitary representations of locally compact groups II, Ann. of Math., to be published. MR 32650
  • 52. F. J. Murray and J. von Neumann, On rings of operators, Ann. of Math. vol. 37 (1935) pp. 116-229.
  • 53. F. J. Murray and J. von Neumann, On rings of operators IV, Ann. of Math. vol. 44 (1943) pp. 716-808. MR 9096
  • 54. J. von Neumann, Almost periodic functions in a group, Trans. Amer. Math. Soc. vol. 36 (1934) pp. 445-492. MR 1501752
  • 55. J. von Neumann, The uniqueness of Haar's measure, Rec. Math. (Mat. Sbornik) N. S. vol. 1 (1936) pp. 721-734.
  • 56. J. von Neumann, Invariant measures, Lecture Notes, Institute for Advanced Study, Princeton, 1941.
  • 57. J. von Neumann, On rings of operators III, Ann. of Math. vol. 41 (1940) pp. 94-161. MR 898
  • 58. J. von Neumann, On rings of operators. Reduction theory, Ann. of Math. vol. 50 (1949) pp. 401-485. MR 29101
  • 59. M. Neumark, Positive definite operator functions on a commutative group, Izvestiya Akademii Nauk SSSR. Ser. Math. vol. 7 (1943) pp. 237-244. MR 10265
  • 60. F. Peter and H. Weyl, Die Vollständigkeit der primitiven Darstellungen einer geschlossene kontinuierlichen Gruppe, Math. Ann. vol. 97 (1927) pp. 737-755. MR 1512386
  • 61. L. Pontrjagin, Les fonctions presque periodiques et l'analysis situs, C. R. Acad. Sci. Paris vol. 196 (1933) pp. 1201-1203.
  • 52. L. Pontrjagin, The theory of topological commutative groups, Ann. of Math. vol. 35 (1934) pp. 361-388. MR 1503168
  • 63. L. Pontrjagin, Topological groups, Princeton, 1939.
  • 64. D. Raikov, Positive definite functions on commutative groups with an invariant measure, C. R. (Doklady) Acad. Sci. URSS. vol. 28 (1940) pp. 296-300. MR 3460
  • 65. D. Raikov, Harmonic analysis on commutative groups with the Haar measure and the theory of characters, Travaux de l'Institut Mathématique Stekloff vol. 14 (1945). MR 17285
  • 66. L. Schwartz, Théorie générale des fonctions moyenne-periodiques, Ann. of Math, vol. 48 (1947) pp. 857-929. MR 23948
  • 67. L. Schwartz, Sur une propriété de synthèse spectrale dans les groupes non compacts, C. R. Acad. Sci. Paris vol. 227 (1948) pp. 424-426. MR 27096
  • 68. I. E. Segal, The group ring of a locally compact group I, Proc. Nat. Acad. Sci. U. S. A. vol. 27 (1941) pp. 348-352. MR 4633
  • 69. I. E. Segal, The group algebra of a locally compact group, Trans. Amer. Math. Soc. vol. 61 (1947) pp. 69-105. MR 19617
  • 70. I. E. Segal, Irreducible representations of operator algebras, Bull. Amer. Math. Soc. vol. 53 (1947) pp. 73-88. MR 20217
  • 71. I. E. Segal, The two sided regular representation of a unimodular locally compact group, Ann. of Math. vol. 51 (1950) pp. 293-298. MR 36764
  • 72. I. E. Segal, A generalization of the Plancherel formula for separable unimodular locally compact groups, to be published.
  • 73. M. H. Stone, On one parameter unitary groups in Hilbert space, Ann. of Math. vol. 33 (1932) pp. 643-648. MR 1503079
  • 74. S. Tannaka, Dualität der nicht-kommutativen Gruppen, Tôhoku Math. J. vol. 53 (1938) pp. 1-12.
  • 75. G. Thorin, An extension of a convexity theorem due to M. Riesz, Kungl. Fysiografiska Sällskopets i Lund Fördhandlingar vol. 8 (1939) no. 14.
  • 76. A. Weil, Sur les fonctions presque périodique de von Neumann, C. R. Acad. Sci. Paris vol. 200 (1935) pp. 38-40.
  • 77. A. Weil, sur les groupes topologiques et les groupes mesures, C. R. Acad. Sci. Paris vol. 202 (1936) pp. 1147-1149.
  • 78. A. Weil, L'intégration dans les groupe topologiques et ses applications, Actualités Scientifique et Industrielles, no. 869, Paris, 1938.
  • 79. H. Weyl, Harmonies on homogeneous manifolds, Ann. of Math. vol. 35 (1934) pp. 486-499. MR 1503175
  • 80. N. Wiener, The Fourier integral and certain of its applications, Cambridge University Press, 1933. MR 983891
  • 81. E. P. Wigner, On unitary representations of the inhomogeneous Lorentz group, Ann. of Math. vol. 40 (1939) pp. 149-204. MR 1503456


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DOI: https://doi.org/10.1090/S0002-9904-1950-09403-8

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