Segal, I. E. Distributions in Hilbert space and canonical systems of operators. (English) Zbl 0099.12104 Trans. Am. Math. Soc. 88, 12-41 (1958); Errata Ibid. 96, 546-547 (1960). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 56 Documents Keywords:probability theory PDF BibTeX XML Cite \textit{I. E. Segal}, Trans. Am. Math. Soc. 88, 12--41 (1958; Zbl 0099.12104) Full Text: DOI References: [1] R. H. Cameron and W. T. Martin, Transformations of Wiener integrals under translations, Ann. of Math. (2) 45 (1944), 386 – 396. · Zbl 0063.00696 · doi:10.2307/1969276 · doi.org [2] 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. · Zbl 0060.29104 [3] P. A. M. Dirac, The Principles of Quantum Mechanics, Oxford, at the Clarendon Press, 1947. 3d ed. · Zbl 0030.04801 [4] K. O. Friedrichs, Mathematical aspects of the quantum theory of fields, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1953. · Zbl 0052.44504 [5] L. Gårding and A. Wightman, Representations of the anticommutation relations, Proc. Nat. Acad. Sci. U. S. A. 40 (1954), 617 – 621. · Zbl 0057.09603 [6] L. Gårding and A. Wightman, Representations of the commutation relations, Proc. Nat. Acad. Sci. U. S. A. 40 (1954), 622 – 626. · Zbl 0057.09604 [7] Shizuo Kakutani, On equivalence of infinite product measures, Ann. of Math. (2) 49 (1948), 214 – 224. · Zbl 0030.02303 · doi:10.2307/1969123 · doi.org [8] F. J. Murray and J. von Neumann, On rings of operators. IV, Ann. of Math. (2) 44 (1943), 716 – 808. · Zbl 0060.26903 · doi:10.2307/1969107 · doi.org [9] I. E. Segal, Decompositions of operator algebras. II, Memoirs of the American Mathematical Society, no. 9, New York 1951. · Zbl 0043.11601 [10] I. E. Segal, A non-commutative extension of abstract integration, Ann. of Math. (2) 57 (1953), 401 – 457. · Zbl 0051.34201 · doi:10.2307/1969729 · doi.org [11] I. E. Segal, Tensor algebras over Hilbert spaces. I, Trans. Amer. Math. Soc. 81 (1956), 106 – 134. · Zbl 0070.34003 [12] I. E. Segal, Tensor algebras over Hilbert spaces. II, Ann. of Math. (2) 63 (1956), 160 – 175. · Zbl 0073.09403 · doi:10.2307/1969994 · doi.org [13] -, Convergent approach to elementary particle interactions, Proc. Nat. Acad. Sci. U.S.A. vol. 42 (1956) pp. 670-676. [14] I. E. Segal, Ergodic subgroups of the orthogonal group on a real Hilbert space, Ann. of Math. (2) 66 (1957), 297 – 303. · Zbl 0083.10603 · doi:10.2307/1970001 · doi.org [15] J. v. Neumann, Die Eindeutigkeit der Schrödingerschen Operatoren, Math. Ann. 104 (1931), no. 1, 570 – 578 (German). · JFM 57.1446.01 · doi:10.1007/BF01457956 · doi.org [16] -, On infinite direct products, Compositio Math. vol. 6 (1938) pp. 1-77. · JFM 64.0377.01 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.