Bulletin of the American Mathematical Society
- Bull. Amer. Math. Soc.
- Volume 71, Number 3, Part 1 (1965), 419-489.
Algebraic integration theory
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Source
Bull. Amer. Math. Soc. Volume 71, Number 3, Part 1 (1965), 419-489.
Dates
First available in Project Euclid: 4 July 2007
Permanent link to this document
http://projecteuclid.org/euclid.bams/1183526903
Mathematical Reviews number (MathSciNet)
MR0178384
Zentralblatt MATH identifier
0135.17402
Citation
Segal, Irving. Algebraic integration theory. Bull. Amer. Math. Soc. 71 (1965), 419--489. http://projecteuclid.org/euclid.bams/1183526903.
References
- 1. W. Ambrose, The L2-system of a unimodular group. I, Trans. Amer. Math. Soc.65 (1949), 27-48.
- 2. R. J. Blattner, Automorphic group representations, Pacific J. Math. 8 (1958), 665-677.Zentralblatt MATH: 0087.32001
Mathematical Reviews (MathSciNet): MR103421
Project Euclid: euclid.pjm/1103039692 - 2A. S. Bochner, Monotone funktionen, Stieltjessche Integrale und harmonische analyse, Math. Ann. 108 (1933), 378-410.
- 3. S. Bochner, Stochastic processes, Ann. of Math. (2) 48 (1947), 1014-1061.Zentralblatt MATH: 0029.36802
Mathematical Reviews (MathSciNet): MR22322
Digital Object Identifier: doi: 10.2307/1969392 - 4. S. Bochner, Harmonic analysis and the theory of probability, Univ. California Press, Berkeley, Calif., 1955.
- 4A. N. Bourbaki, Éléments de mathématique. XIII, Hermann, Paris, 1952.
- 5. R. H. Cameron, The translation pathology of Wiener space, Duke Math. J. 21 (1954), 623-627.Zentralblatt MATH: 0057.09601
Mathematical Reviews (MathSciNet): MR65033
Digital Object Identifier: doi: 10.1215/S0012-7094-54-02165-1
Project Euclid: euclid.dmj/1077466012 - 6. R. H. Cameron and W. T. Martin, Transformations of Wiener integrals under translations, Ann. of Math. (2) 45 (1944), 386-396.Zentralblatt MATH: 0063.00696
Mathematical Reviews (MathSciNet): MR10346
Digital Object Identifier: doi: 10.2307/1969276 - 7. R. H. Cameron and W. T. Martin, An expression for the solution of a class of non-linear integral equations, Amer. J. Math. 66 (1944), 281-298.Zentralblatt MATH: 0063.00697
Mathematical Reviews (MathSciNet): MR10050
Digital Object Identifier: doi: 10.2307/2371988 - 8. R. H. Cameron and W. T. Martin, Transformations of Wiener integrals under a general class of linear transformations, Trans. Amer. Math. Soc. 58 (1945), 184-219.
- 9. R. H. Cameron and W. T. Martin, Fourier-Wiener transforms of functionals belonging to L2 over the space C, Duke Math. J. 14 (1947), 99-107.Zentralblatt MATH: 0029.40002
Mathematical Reviews (MathSciNet): MR20231
Digital Object Identifier: doi: 10.1215/S0012-7094-47-01409-9
Project Euclid: euclid.dmj/1077473992 - 10. R. H. Cameron and W. T. Martin, The behavior of measure and measurability under change of scale in Wiener space, Bull. Amer. Math. Soc. 53 (1947), 130-137.Zentralblatt MATH: 0032.41801
Mathematical Reviews (MathSciNet): MR19259
Digital Object Identifier: doi: 10.1090/S0002-9904-1947-08762-0
Project Euclid: euclid.bams/1183510407 - 11. R. H. Cameron and W. T. Martin, The transformation of Wiener integrals by non-linear transformations, Trans. Amer. Math. Soc. 66 (1949), 253-283.Zentralblatt MATH: 0035.07302
Mathematical Reviews (MathSciNet): MR31196
Digital Object Identifier: doi: 10.1090/S0002-9947-1949-0031196-6 - 12. C. Carathéodory, Mass und Integral und ihre Algebraisierung, Birkhäuser Verlag, Basel and Stuttgart, 1956.
- 12A. J. M. Cook, The mathematics of second quantization, Trans. Amer. Math. Soc. 74 (1957), 222-245.Zentralblatt MATH: 0052.22701
Mathematical Reviews (MathSciNet): MR53784
Digital Object Identifier: doi: 10.1090/S0002-9947-1953-0053784-4 - 13. P. J. Daniell, A general form of integral, Ann. of Math. (2) 19 (1917/18), 279-294.
- 14. P. A. M. Dirac, The principles of quantum mechanics, 3rd ed., Oxford Univ. Press, Oxford, 1947.
- 15. J. Dixmier, Les fonctionnelles linéaires sur l'ensemble des opérateurs bornés d'un espace de Hilbert, Ann. of Math. (2) 51 (1950), 387-408.Zentralblatt MATH: 0036.35801
Mathematical Reviews (MathSciNet): MR33445
Digital Object Identifier: doi: 10.2307/1969331 - 16. J. Dixmier, Sur certaines espaces considérés par M. H. Stone, Summa Brasil. Math. 2 (1951), 151-182.
- 17. J. Dixmier, Formes linéaires sur un anneau d'opérateurs, Bull. Soc. Math. France 81 (1953), 9-39.
- 17A. J. Dixmier, Algèbres quasi-unitaires, Comment. Math. Helv. 26 (1952), 275-322.Zentralblatt MATH: 0047.35601
Mathematical Reviews (MathSciNet): MR52697
Digital Object Identifier: doi: 10.1007/BF02564306 - 18. J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien, Gauthier-Villars, Paris, 1957
- 19. H. A. Dye, The Radon-Nikodým theorem for finite rings of operators, Trans. Amer. Math. Soc. 72 (1952), 243-280.
- 20. J. Feldman, On the Schrödinger and heat equations for bad potentials, Trans. Amer. Math. Soc. 108 (1963), 251-264.
- 21. R. P. Feynman, Space-time approach to non-relativistic quantum mechanics, Rev. Modern Phys. 20 (1948), 367-387.Mathematical Reviews (MathSciNet): MR26940
Digital Object Identifier: doi: 10.1103/RevModPhys.20.367 - 22. R. P. Feynman, An operator calculus having applications in quantum electrodynamics, Phys. Rev. (2) 84 (1951), 108-128.Zentralblatt MATH: 0044.23304
Mathematical Reviews (MathSciNet): MR44379
Digital Object Identifier: doi: 10.1103/PhysRev.84.108 - 23. K. O. Friedrichs, Mathematical aspects of the quantum theory of fields, Interscience, New York, 1953.
- 24. K. O. Friedrichs and H. N. Shapiro, Integration over Hilbert space and outer extensions, Proc. Nat. Acad. Sci. U.S.A. 43 (1957), 336-338.Zentralblatt MATH: 0077.31303
Mathematical Reviews (MathSciNet): MR108711
Digital Object Identifier: doi: 10.1073/pnas.43.4.336 - 25. K. O. Friedrichs and colleagues, Seminar on Integration of Functionals, Mimeographed notes published by New York University, Institute of Mathematical Sciences, 1957.Zentralblatt MATH: 0315.28008
- 26. H. Furstenberg, Stationary processes and prediction theory, Princeton Univ. Press, Princeton, N. J., 1960.
- 27. I. M. Gelfand, Normierte Ringe, Mat. Sb. (N.S.) 9 (51) (1941), 3-24.Mathematical Reviews (MathSciNet): MR4726
- 28. I. M. Gelfand, Generalized random processes, Dokl. Akad. Nauk SSSR 100 (1955), 853-856. (Russian)Mathematical Reviews (MathSciNet): MR68769
- 29. I. M. Gelfand and M. A. Naĭmark, Unitary representations of the Lorentz group, Izv. Akad. Nauk SSSR Ser. Mat. 11 (1947), 411-504. (Russian)
- 30. I. M. Gelfand and M. A. Naĭmark, Unitary representations of the classical groups, Trudy Mat. Inst. Steklov., Vol. 36, Izdat. Akad. Nauk SSSR, Moscow, 1950. (Russian)Mathematical Reviews (MathSciNet): MR46370
- 31. I. M. Gelfand and M. I. Graev, Analogue of the Plancherel formula for the classical groups, Trudy Moskov. Mat. Obšč. 4 (1955), 375-404 (Russian); Amer. Math. Soc. Transl. (2) 9 (1958), 123-154.
- 32. I. M. Gelfand, D. A. Rykov, and G. E. Shilov, Commutative normed rings, Uspehi Mat. Nauk 1 (1946), 48-146 (Russian); Amer. Math. Soc. Transl. (2) 5(1957), 115-220.
- 33. I. M. Gelfand and N. Y. Vilenkin, Generalized functions, Vol. 4, Moscow, 1961.
- 34. I. M. Gelfand and A. M. Yaglom, Integration in functional spaces and its applications in quantum physics, J. Mathematical Phys. 1 (1960), 48-69.Zentralblatt MATH: 0092.45105
Mathematical Reviews (MathSciNet): MR112604
Digital Object Identifier: doi: 10.1063/1.1703636 - 35. A. M. Gleason, Measures on the closed subspaces of a Hilbert space, J. Math. Mech. 6 (1957), 885-893.
- 36. R. Godement, Sur la théorie des représentations unitaires, Ann. of Math. (2)53 (1951), 68-124.Zentralblatt MATH: 0042.34606
Mathematical Reviews (MathSciNet): MR38571
Digital Object Identifier: doi: 10.2307/1969343 - 37. R. Godement, Théorie des caractères. I. Algèbres unitaires, Ann. of Math. (2) 59 (1954), 47-62.Zentralblatt MATH: 0055.02103
Mathematical Reviews (MathSciNet): MR58879
Digital Object Identifier: doi: 10.2307/1969832 - 38. E. L. Griffin, Jr., Some contributions to the theory of rings of operators, Trans. Amer. Math. Soc. 75 (1953), 471-504; II, ibid. 79 (1955), 389-400.Zentralblatt MATH: 0065.34904
Mathematical Reviews (MathSciNet): MR59487
Digital Object Identifier: doi: 10.1090/S0002-9947-1953-0059487-4 - 39. L. Gross, Integration and non-linear transformations in Hilbert space, Trans. Amer. Math. Soc. 94 (1960), 404-440.Zentralblatt MATH: 0090.33303
Mathematical Reviews (MathSciNet): MR112025
Digital Object Identifier: doi: 10.1090/S0002-9947-1960-0112025-3 - 40. L. Gross, Measurable functions on Hilbert space, Trans. Amer. Math. Soc. 105 (1962), 372-390.Zentralblatt MATH: 0178.50001
Mathematical Reviews (MathSciNet): MR147606
Digital Object Identifier: doi: 10.1090/S0002-9947-1962-0147606-6 - 41. L. Gross, Harmonic analysis on Hilbert space, Mem. Amer. Math. Soc. No. 46 (1963).
- 42. L. Gross, Classical analysis on a Hilbert space, Proc. Conf. Analysis in Function Space, Cambridge, Mass., 1964, pp. 51-68.Mathematical Reviews (MathSciNet): MR167150
- 43. Harish-Chandra, The Plancherel formula for complex semisimple Lie groups, Trans. Amer. Math. Soc. 76 (1954), 485-528.Zentralblatt MATH: 0055.34003
Mathematical Reviews (MathSciNet): MR63376
Digital Object Identifier: doi: 10.1090/S0002-9947-1954-0063376-X - 44. K. Ito, Stationary random distributions, Mem. Coll. Sci. Univ. Kyoto 28 (1953), 209-223.
- 45. M. Kac, Probability and related topics in physical science, Proc. Summer Seminar, Boulder, Colo., 1957, Vol. I, Interscience, New York, 1959.
- 46. R. V. Kadison, On the additivity of the trace in finite factors, Proc. Nat. Acad Sci. U.S.A. 41 (1955), 385-387.Zentralblatt MATH: 0064.36604
Mathematical Reviews (MathSciNet): MR69402
Digital Object Identifier: doi: 10.1073/pnas.41.6.385 - 47. S. Kakutani, Concrete representation of abstract (L)-spaces and the mean ergodic theorem, Ann. of Math. (2) 42 (1941), 523-537.Zentralblatt MATH: 0027.11102
Mathematical Reviews (MathSciNet): MR4095
Digital Object Identifier: doi: 10.2307/1968915 - 48. S. Kakutani, Determination of the spectrum of the flow of Brownian motion, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 319-323.Zentralblatt MATH: 0038.29105
Mathematical Reviews (MathSciNet): MR35924
Digital Object Identifier: doi: 10.1073/pnas.36.5.319 - 48A. S. Kakutani, Spectral analysis of stationary Gaussian processes, Proc. 4th Berkeley Sympos. Probability, Vol. 2, 1961; pp. 239-247.
- 49. A. Kirillov, Unitary representations of nilpotent Lie groups, Russian Math. Surveys 17 (1962), 53-104.
- 50. A. Kolmogoroff, Grundbegriffe der Wahrscheinlichkeitsrechnung, Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer, Berlin, 1933; pp. 1-62.
- 51. R. A. Kunze, Lp-Fourier transforms on locally compact unimodular groups, Trans. Amer. Math. Soc. 89 (1958), 519-540.
- 52. C. Loewner, Grundzüge einer Inhaltlehre im Hilbertschen Raume, Ann. of Math.(2) 40 (1939), 816-833.
- 53. L. H. Loomis, On the representation of $\sigma$-complete Boolean algebras, Bull. Amer. Math. Soc. 63 (1947), 757-760.Zentralblatt MATH: 0033.01103
Mathematical Reviews (MathSciNet): MR21084
Digital Object Identifier: doi: 10.1090/S0002-9904-1947-08866-2
Project Euclid: euclid.bams/1183510979 - 54. L. H. Loomis, Note on a theorem of Mackey, Duke Math. J. 19 (1952), 641-645.Zentralblatt MATH: 0047.35501
Mathematical Reviews (MathSciNet): MR50596
Digital Object Identifier: doi: 10.1215/S0012-7094-52-01968-6
Project Euclid: euclid.dmj/1077477513 - 55. G. W. Mackey, A theorem of Stone and von Neumann, Duke Math. J. 16 (1949), 313-326.Zentralblatt MATH: 0036.07703
Mathematical Reviews (MathSciNet): MR30532
Digital Object Identifier: doi: 10.1215/S0012-7094-49-01631-2
Project Euclid: euclid.dmj/1077475512 - 56. G. W. Mackey, Imprimitivity for representations of locally compact groups. I, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 537-545.Zentralblatt MATH: 0035.06901
Mathematical Reviews (MathSciNet): MR31489
Digital Object Identifier: doi: 10.1073/pnas.35.9.537 - 57. G. W. Mackey, Induced representations of locally compact groups. II. The Frobenius reciprocity theorem, Ann. of Math. (2) 58 (1953), 193-221.Zentralblatt MATH: 0051.01901
Mathematical Reviews (MathSciNet): MR56611
Digital Object Identifier: doi: 10.2307/1969786 - 58. G. W. Mackey, Unitary representations of group extensions. I, Acta Math. 99 (1958), 265-371.Zentralblatt MATH: 0082.11301
Mathematical Reviews (MathSciNet): MR98328
Digital Object Identifier: doi: 10.1007/BF02392428 - 59. G. W. Mackey, Point realizations of transformation groups, Illinois J. Math. 6 (1962), 327-335.Zentralblatt MATH: 0178.17203
Mathematical Reviews (MathSciNet): MR143874
Project Euclid: euclid.ijm/1255632330 - 60. D. Maharam, Homogeneous measure algebras, Proc. Nat. Acad. Sci. U.S.A. 28 (1941), 108-111.Zentralblatt MATH: 0063.03723
Mathematical Reviews (MathSciNet): MR6595
Digital Object Identifier: doi: 10.1073/pnas.28.3.108 - 61. D. Maharam, An algebraic characterization of measure algebras, Ann. of Math. (2) 48 (1947), 154-167.Zentralblatt MATH: 0029.20401
Mathematical Reviews (MathSciNet): MR18718
Digital Object Identifier: doi: 10.2307/1969222 - 62. F. Mautner, Unitary representations of locally compact groups. II, Ann. of Math. (2) 52 (1950), 528-556.Zentralblatt MATH: 0039.02201
Mathematical Reviews (MathSciNet): MR36763
Digital Object Identifier: doi: 10.2307/1969431 - 63. F. Mautner, On eigenfunction expansions, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 49-53.Zentralblatt MATH: 0050.11901
Mathematical Reviews (MathSciNet): MR52690
Digital Object Identifier: doi: 10.1073/pnas.39.1.49 - 64. E. J. McShane, Remark concerning integration, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 46-49.Zentralblatt MATH: 0032.15002
Mathematical Reviews (MathSciNet): MR27831
Digital Object Identifier: doi: 10.1073/pnas.35.1.46 - 65. E. J. McShane, Integrals devised for special purposes, Bull. Amer. Math. Soc. 69 (1963), 597-627.Zentralblatt MATH: 0116.04202
Mathematical Reviews (MathSciNet): MR162905
Digital Object Identifier: doi: 10.1090/S0002-9904-1963-10964-7
Project Euclid: euclid.bams/1183525452 - 65A. J. Milkman, Hermite polynomials, Hermite functionals and their integrals in real Hilbert space, Riv. Mat. Univ. Parma 6 (1955), 65-88.
- 66. F. J. Murray and J. von Neumann, On rings of operators, Ann. of Math. 37 (1936), 116-229.Zentralblatt MATH: 0014.16101
Mathematical Reviews (MathSciNet): MR1503275
Digital Object Identifier: doi: 10.2307/1968693 - 67. F. J. Murray and J. von Neumann, On rings of operators. II, Trans. Amer. Math. Soc. 41 (1937), 208-248.Mathematical Reviews (MathSciNet): MR1501899
Digital Object Identifier: doi: 10.1090/S0002-9947-1937-1501899-4 - 68. F. J. Murray and J. von Neumann, On rings of operators. IV, Ann. of Math. (2) 44 (1943), 716-808.Zentralblatt MATH: 0060.26903
Mathematical Reviews (MathSciNet): MR9096
Digital Object Identifier: doi: 10.2307/1969107 - 69. M. Nakamura and H. Umegaki, On a proposition of von Neumann, Kodai Math. Sem. Rep. 8 (1956), 142-144.Zentralblatt MATH: 0073.33301
Mathematical Reviews (MathSciNet): MR90790
Digital Object Identifier: doi: 10.2996/kmj/1138843772
Project Euclid: euclid.kmj/1138843772 - 70. H. Nakano, Hilbert algebras, Tôhoku Math. J. 2 (1950), 4-23.Zentralblatt MATH: 0041.23501
Mathematical Reviews (MathSciNet): MR41362
Digital Object Identifier: doi: 10.2748/tmj/1178245666
Project Euclid: euclid.tmj/1178245666 - 71. Edward Nelson, Feynman integrals and the Schrödinger equation, J. Mathematical Phys. 5 (1964), 332-343.Zentralblatt MATH: 0133.22905
Mathematical Reviews (MathSciNet): MR161189
Digital Object Identifier: doi: 10.1063/1.1704124 - 72. 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.
- 73. R. Pallu de la Barrière, Algèbres unitaires et espaces d'Ambrose, Ann. Sci. École Norm. Sup. (3) 70 (1953), 381-401.
- 73A. R. Pallu de la Barrière, Sur les algèbres d'opérateurs dans les espaces hilbertiens, Bull. Soc. Math. France 82 (1954), 1-52.
- 74. M. Plancherel, Contribution à l'étude de la représentation d'une fonction arbitraire par des integrals définie, Rend. Circ. Mat. Palermo 30 (1910), 289-335.
- 75. A. Plessner, Eine Kennzeichnung der total-stetigen Funktionen, J. Reine Angew. Math. 160 (1929), 26-32.
- 76. Y. V. Prohorov, The method of characteristic functionals, Proc. 4th Berkeley Sympos. Probability, Vol. 2, 1961; pp. 403-420.
- 77. L. Pukanszky, The theorem of Radon-Nikodým in operator-rings, Acta Sci. Math. (Szeged) 15 (1954), 149-156.
- 77A. V. A. Rokhlin, Unitary rings, Dokl. Akad. Nauk SSSR 59 (1948), 643-646.
- 78. Proceedings of the Symposium on Time Series Analysis, M. Rosenblatt, editor, pp. 279-348, Wiley, New York, 1963.Mathematical Reviews (MathSciNet): MR145634
- 79. D. A. Rykov, Harmonic analysis on commutative groups, Trudy Mat. Inst. Steklov. 14 (1945).
- 80. S. Saks, Theory of the integral, 2nd ed.; Note II by S. Banach, Lebesgue integration in abstract spaces, pp. 320-330.Mathematical Reviews (MathSciNet): MR167578
- 81. V. Sazonov, On characteristic functionals, Teor. Verojatnost. i Primenen. 3 (1958), 201-205.
- 82. R. Schatten, The space of completely continuous operators on a Hilbert space, Math. Ann. 134 (1957), 47-49.Zentralblatt MATH: 0079.12801
Mathematical Reviews (MathSciNet): MR90021
Digital Object Identifier: doi: 10.1007/BF01342831 - 83. I. Segal, Postulates for general quantum mechanics, Ann. of Math. (2) 48 (1947), 930-948.Zentralblatt MATH: 0034.06602
Mathematical Reviews (MathSciNet): MR22652
Digital Object Identifier: doi: 10.2307/1969387 - 84. I. Segal, A kind of abstract integration pertinent to locally compact groups. I, Abstract, Bull. Amer. Math. Soc. 55 (1949), 46.
- 85. I. Segal, The two-sided regular representation of a unimodular locally compact group, Ann. of Math. (2) 51 (1950), 293-298.Zentralblatt MATH: 0039.02103
Mathematical Reviews (MathSciNet): MR36764
Digital Object Identifier: doi: 10.2307/1969325 - 86. I. Segal, An extension of Plancherel's formula to separable unimodular groups, Ann. of Math. (2) 52 (1950), 272-292.Zentralblatt MATH: 0045.38502
Mathematical Reviews (MathSciNet): MR36765
Digital Object Identifier: doi: 10.2307/1969470 - 87. I. Segal, Decompositions of operator algebras. I, II. Multiplicity theory, Mem. Amer. Math. Soc. No. 9, (1951).
- 88. I. Segal, A non-commutative extension of abstract integration, Ann. of Math. (2) 57 (1953), 401-457.Zentralblatt MATH: 0051.34201
Mathematical Reviews (MathSciNet): MR54864
Digital Object Identifier: doi: 10.2307/1969729 - 89. I. Segal, Abstract probability spaces and a theorem of Kolmogoroff, Amer. J. Math. 76 (1954), 721-732.Zentralblatt MATH: 0056.12301
Mathematical Reviews (MathSciNet): MR63602
Digital Object Identifier: doi: 10.2307/2372714 - 90. I. Segal, Tensor algebras over Hilbert spaces, Trans. Amer. Math. Soc. 81 (1956), 106-134.Zentralblatt MATH: 0070.34003
Mathematical Reviews (MathSciNet): MR76317
Digital Object Identifier: doi: 10.1090/S0002-9947-1956-0076317-8 - 91. I. Segal, Tensor algebras over Hilbert spaces. II, Ann. of Math. (2) 63 (1956), 160-175.Zentralblatt MATH: 0073.09403
Mathematical Reviews (MathSciNet): MR77908
Digital Object Identifier: doi: 10.2307/1969994 - 92. I. Segal, Ergodic subgroups of the orthogonal group on a real Hilbert space, Ann. of Math. (2) 66 (1957), 297-303.Zentralblatt MATH: 0083.10603
Mathematical Reviews (MathSciNet): MR89382
Digital Object Identifier: doi: 10.2307/1970001 - 93. I. Segal, Equivalences of measure spaces, Amer. J. Math. 73 (1951), 275-313.Zentralblatt MATH: 0042.35502
Mathematical Reviews (MathSciNet): MR41191
Digital Object Identifier: doi: 10.2307/2372178 - 94. I. Segal, Distributions in Hilbert space and canonical systems of operators, Trans. Amer. Math. Soc. 88 (1958), 12-41.Zentralblatt MATH: 0099.12104
Mathematical Reviews (MathSciNet): MR102759
Digital Object Identifier: doi: 10.1090/S0002-9947-1958-0102759-X - 95. I. Segal, A theorem on the measurability of group-invariant operators, Duke Math. J. 26 (1959), 549-552.Zentralblatt MATH: 0092.32104
Mathematical Reviews (MathSciNet): MR110955
Digital Object Identifier: doi: 10.1215/S0012-7094-59-02651-1
Project Euclid: euclid.dmj/1077468763 - 95A. I. Segal, Foundations of the theory of dynamical systems of infinitely many degrees of freedom. I, Mat. Fys. Medd. Danske Vid. Selsk. 31 (1959), no. 12.
- 96. I. Segal, Transforms for operators and symplectic automorphisms over a locally compact abelian group, Math. Scand. 13 (1963), 31-43.
- 97. I. Segal, Mathematical problems of relativistic physics, Lectures in Applied Mathematics, Amer. Math. Soc., Providence, R. I., 1963.
- 98. T. I. Seidman, Linear transformations of a functional integral, Comm. Pure Appl. Math. 12 (1959), 611-621; correction, ibid. 16 (1963), 95-96; II, ibid. 17(1964), 493-508.Zentralblatt MATH: 0139.07902
Mathematical Reviews (MathSciNet): MR110009
Digital Object Identifier: doi: 10.1002/cpa.3160120404 - 99. D. Shale, Linear symmetries of free boson fields, Trans. Amer. Math. Soc.103 (1962), 149-167.Zentralblatt MATH: 0171.46901
Mathematical Reviews (MathSciNet): MR137504
Digital Object Identifier: doi: 10.1090/S0002-9947-1962-0137504-6 - 100. D. Shale and W. F. Stinespring, States of the Clifford algebra, Ann. of Math.(2) 80 (1964), 365-381.Zentralblatt MATH: 0178.49301
Mathematical Reviews (MathSciNet): MR165880
Digital Object Identifier: doi: 10.2307/1970397 - 101. W. F. Stinespring, Integration theorems for gages and duality for unimodular groups, Trans. Amer. Math. Soc. 90 (1959), 15-56.Zentralblatt MATH: 0085.10202
Mathematical Reviews (MathSciNet): MR102761
Digital Object Identifier: doi: 10.1090/S0002-9947-1959-0102761-9 - 102. M. H. Stone, Linear transformations in Hilbert space, Amer. Math. Soc. Colloq. Publ. Vol. 15, Amer. Math. Soc., Providence, R. I., 1932.
- 102A. M. H. Stone, On one-parameter unitary groups in Hilbert space, Ann. of Math. 33 (1932), 643-648.Zentralblatt MATH: 0005.16403
Mathematical Reviews (MathSciNet): MR1503079
Digital Object Identifier: doi: 10.2307/1968538 - 103. M. H. Stone, The theory of representations of Boolean algebras, Trans. Amer. Math. Soc. 40 (1936), 37-111.Mathematical Reviews (MathSciNet): MR1501865
- 104. M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), 375-481.Mathematical Reviews (MathSciNet): MR1501905
Digital Object Identifier: doi: 10.1090/S0002-9947-1937-1501905-7 - 105. M. H. Stone, Notes on integration. I, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 336-342; II, ibid. 34 (1948), 447-455; III, ibid. 34 (1948), 483-490; IV, ibid. 35(1949), 50-58.Zentralblatt MATH: 0034.03001
Mathematical Reviews (MathSciNet): MR25552
Digital Object Identifier: doi: 10.1073/pnas.34.7.336 - 106. M. H. Stone, A general theory of spectra. I, Proc. Nat. Acad. Sci. U.S.A. 26 (1940), 280-283; II, ibid. 27 (1941), 83-87.
- 107. J. von Neumann, Die Eindeutigkeit der Schrödingerschen Operatoren, Math. Ann. 104 (1941), 570-578.Zentralblatt MATH: 0001.24703
Mathematical Reviews (MathSciNet): MR1512685
Digital Object Identifier: doi: 10.1007/BF01457956 - 108. J. von Neumann, Über Funktionen von Funktionaloperatoren, Ann. of Math. 32 (1931), 191-226.Zentralblatt MATH: 0002.26703
Mathematical Reviews (MathSciNet): MR1502991
Digital Object Identifier: doi: 10.2307/1968185 - 109. J. von Neumann, Mathematische Grundlagen der Quantenmechanik, Springer, Berlin, 1932.Mathematical Reviews (MathSciNet): MR223138
- 109A. J. von Neumann, Approximative properties of matrices of high order, Portugal. Math. 3 (1942), 1-62.Mathematical Reviews (MathSciNet): MR6137
- 110. J. von Neumann, On an algebraical generalization of the quantum mechanical formalism. I, Mat. Sb. (N.S.) 1 (437) (1936), 415-484.
- 111. J. von Neumann, On rings of operators. III, Ann. of Math. 41 (1940), 94-161.Zentralblatt MATH: 0023.13303
Mathematical Reviews (MathSciNet): MR898
Digital Object Identifier: doi: 10.2307/1968823 - 112. J. von Neumann, On rings of operators. Reduction theory, Ann. of Math. (2) 50 (1949), 401-485.Zentralblatt MATH: 0034.06102
Mathematical Reviews (MathSciNet): MR29101
Digital Object Identifier: doi: 10.2307/1969463 - 113. A. Weil, L'intégration dans les groupes topologiques et ses applications, Hermann, Paris, 1938.Zentralblatt MATH: 0063.08195
- 114. A. Weil, Sur certains groupes d'opérateurs unitaires, Acta Math. 111 (1964), 247-302.Zentralblatt MATH: 0203.03305
Mathematical Reviews (MathSciNet): MR165033
Digital Object Identifier: doi: 10.1007/BF02391012 - 115. N. Wiener, Differential space, J. Math. Phys. M.I.T. 2 (1923), 131-174.
- 116. N. Wiener, The homogeneous chaos, Amer. J. Math. 60 (1938), 896-936.
- 117. N. Wiener, The Fourier integral and certain of its applications, Cambridge Univ. Press, Cambridge, 1933.
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