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)

 
 

 

Distributions in Hilbert space and canonical systems of operators


Author: I. E. Segal
Journal: Trans. Amer. Math. Soc. 88 (1958), 12-41
MSC: Primary 46.00; Secondary 81.00
DOI: https://doi.org/10.1090/S0002-9947-1958-0102759-X
Erratum: Trans. Amer. Math. Soc. 96 (1960), 546-546.
MathSciNet review: 0102759
Full-text PDF Free Access

References | Similar Articles | Additional Information

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

  • [1] R. H. Cameron and W. T. Martin, Transformation of Wiener integrals under translations, Ann. of Math. vol. 45 (1944) pp. 386-396. MR 0010346 (6:5f)
  • [2] -, Transformation of Wiener integrals under a general class of linear transformations, Trans. Amer. Math. Soc. vol. 58 (1945) pp. 184-219. MR 0013240 (7:127c)
  • [3] P. A. M. Dirac, The principles of quantum mechanics, 3d ed., Oxford, 1947. MR 0023198 (9:319d)
  • [4] K. O. Friedrichs, Mathematical aspects of the quantum theory of fields, New York, 1953. MR 0056468 (15:80c)
  • [5] L. Gårding and A. S. Wightman, Representations of the anticommutation relations, Proc. Nat. Acad. Sci. U.S.A. vol. 40 (1954) pp. 617-621. MR 0062956 (16:49a)
  • [6] -, Representations of the commutation relations, Proc. Nat. Acad. Sci. U.S.A. vol. 40 (1954) pp. 622-626. MR 0062957 (16:49b)
  • [7] S. Kakutani, On equivalence of infinite product measures, Ann. of Math. vol. 49 (1948) pp. 214-224. MR 0023331 (9:340e)
  • [8] F. J. Murray and J. von Neumann, On rings of operators IV, Ann. of Math. vol. 44 (1943) pp. 716-808. MR 0009096 (5:101a)
  • [9] I. E. Segal, Decompositions of operator algebras. II, Memoirs of the American Mathematical Society, no. 9, New York 1951.
  • [10] -, A non-commutative extension of abstract integration, Ann. of Math. vol. 57 (1953) pp. 401-457. MR 0054864 (14:991f)
  • [11] -, Tensor algebras over Hilbert spaces. I, Trans. Amer. Math. Soc. vol. 81 (1956) pp. 106-134. MR 0076317 (17:880d)
  • [12] -, Tensor algebras over Hilbert spaces. II, Ann. of Math. vol. 63 (1956) pp. 160-175. MR 0077908 (17:1114f)
  • [13] -, Convergent approach to elementary particle interactions, Proc. Nat. Acad. Sci. U.S.A. vol. 42 (1956) pp. 670-676.
  • [14] -, Ergodic subgroups of the orthogonal group on a real Hilbert space, Ann. of Math. vol. 66 (1957) pp. 297-303. MR 0089382 (19:666d)
  • [15] J. von Neumann, Die eindeutigkeit der Schrödingerschen Operatoren, Math. Ann. vol. 104 (1931) pp. 570-578. MR 1512685
  • [16] -, On infinite direct products, Compositio Math. vol. 6 (1938) pp. 1-77.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46.00, 81.00

Retrieve articles in all journals with MSC: 46.00, 81.00


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1958-0102759-X
Article copyright: © Copyright 1958 American Mathematical Society

American Mathematical Society