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)

 
 

 

Spectral theory for semi-groups of linear operators


Author: R. S. Phillips
Journal: Trans. Amer. Math. Soc. 71 (1951), 393-415
MSC: Primary 46.3X
DOI: https://doi.org/10.1090/S0002-9947-1951-0044737-9
MathSciNet review: 0044737
Full-text PDF Free Access

References | Similar Articles | Additional Information

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

  • [1] Warren Ambrose, Spectral resolution of groups of unitary operators, Duke Math. J. vol. 11 (1944) pp. 589-595. MR 0011172 (6:131c)
  • [2] A. Beurling, Sur les intégrales de Fourier absolument convergentes et leur application à une transformation fonctionelle, Neuvième Congrès Math. Scand. Helsingfors, 1938, pp. 345-366.
  • [3] I. Gelfand, Normierte Ringe, Rec. Math. (Mat. Sbornik) N.S. vol. 9 (1941) pp. 3-24. MR 0004726 (3:51f)
  • [4] -, Zur Theorie der Charaktere der Abelschen topologischen Gruppen, Rec. Math. (Mat. Sbornik) N.S. vol. 9 (1941) pp. 49-50. MR 0004635 (3:36d)
  • [5] -, Über absolut konvergente trigonometrische Reihen und Integrale, Rec. Math. (Mat. Sbornik) N.S. vol. 9 (1941) pp. 51-66. MR 0004727 (3:51g)
  • [6] Einar Hille, Functional analysis and semi-groups, Amer. Math. Soc. Colloquium Publications, vol. 31, New York, 1948. MR 0025077 (9:594b)
  • [7] -, On the differentiability of semi-group operators, Acta Univ. Szeged. vol. 12 (1950) part B, pp. 19-24. MR 0036445 (12:110a)
  • [8] B. v. Sz. Nagy, Spektraldarstellung linearer Transformationen des Hilbertschen Raumes, Ergebnisse der Mathematik, vol. 5, Berlin, 1942.
  • [9] M. Neumark, Positive definite Operator functions on a commutative group, Bull. Acad. Sci. URSS. vol. 7 (1943) pp. 237-244. MR 0010265 (5:272c)
  • [10] R. S. Phillips, On semi-groups of operators, Proceedings of the American Mathematical Society vol. 2 (1951) pp. 234-237.
  • [11] M. Stone, On one parameter unitary groups in Hilbert spaces, Ann. of Math. vol. 33 (1932) pp. 643-648. MR 1503079
  • [12] -, A general theory of spectra I, Proc. Nat. Acad. Sci. U.S.A. vol. 26 (1940) pp. 280-283. MR 0002023 (1:338e)
  • [13] -, A general theory of spectra II, Proc. Nat. Acad. Sci. U.S.A. vol. 27 (1941) pp. 83-87. MR 0004092 (2:318a)
  • [14] -, Boundedness properties in function-lattices, Canadian Journal of Mathematics vol. 1 (1949) pp. 176-186. MR 0029091 (10:546a)
  • [15] -, On a theorem of Pólya, J. Indian Math. Soc. N.S. vol. 12 (1948) pp. 1-7.
  • [16] I. Vernikoff, S. Krein, and A. Tovbin, Sur les anneaux semi-ordonnés, C. R. (Doklady) Acad. Sci. URSS. N.S. vol. 30 (1941) pp. 785-787. MR 0004072 (2:314e)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46.3X

Retrieve articles in all journals with MSC: 46.3X


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1951-0044737-9
Article copyright: © Copyright 1951 American Mathematical Society

American Mathematical Society