The group algebra of a locally compact group

The group algebra of a locally compact group
HTML articles powered by AMS MathViewer

by I. E. Segal

Trans. Amer. Math. Soc. 61 (1947), 69-105

DOI: https://doi.org/10.1090/S0002-9947-1947-0019617-4

PDF | Request permission

References

Ralph Palmer Agnew, Spans in Lebesgue and uniform spaces of translations of step functions, Bull. Amer. Math. Soc. 51 (1945), 229–233. MR 12159, DOI 10.1090/S0002-9904-1945-08313-X
Ralph Palmer Agnew, Spans in Lebesgue and uniform spaces of translations of peak function, Amer. J. Math. 67 (1945), 431–436. MR 12699, DOI 10.2307/2371957
Warren Ambrose, Structure theorems for a special class of Banach algebras, Trans. Amer. Math. Soc. 57 (1945), 364–386. MR 13235, DOI 10.1090/S0002-9947-1945-0013235-8

Sur les intégrales de Fourier absolument convergentes et leur application à une transformation fonctionelle

J. W. Calkin, Two-sided ideals and congruences in the ring of bounded operators in Hilbert space, Ann. of Math. (2) 42 (1941), 839–873. MR 5790, DOI 10.2307/1968771
R. H. Cameron and Norbert Wiener, Convergence properties of analytic functions of Fourier-Stieltjes transforms, Trans. Amer. Math. Soc. 46 (1939), 97–109. MR 72, DOI 10.1090/S0002-9947-1939-0000072-0

Une inégalité

V. Ditkin, On the structure of ideals in certain normed rings, Uchenye Zapiski Moskov. Gos. Univ. Matematika 30 (1939), 83–130 (Russian, with English summary). MR 0002012
Nelson Dunford and B. J. Pettis, Linear operations on summable functions, Trans. Amer. Math. Soc. 47 (1940), 323–392. MR 2020, DOI 10.1090/S0002-9947-1940-0002020-4

On normed rings

I. Gelfand, To the theory of normed rings. II. On absolutely convergent trigonometrical series and integrals, C. R. (Doklady) Acad. Sci. URSS (N.S.) 25 (1939), 570–572. MR 0001984
I. Gelfand, Ideale und primäre Ideale in normierten Ringen, Rec. Math. [Mat. Sbornik] N.S. 9 (51) (1941), 41–48 (German, with Russian summary). MR 0004728
I. Gelfand, Normierte Ringe, Rec. Math. [Mat. Sbornik] N.S. 9 (51) (1941), 3–24 (German, with Russian summary). MR 0004726
I. Gelfand, Über absolut konvergente trigonometrische Reihen und Integrale, Rec. Math. [Mat. Sbornik] N.S. 9 (51) (1941), 51–66 (German, with Russian summary). MR 0004727
I. Gelfand and D. Raikov, On the theory of characters of commutative topological groups, C. R. (Doklady) Acad. Sci. URSS (N.S.) 28 (1940), 195–198. MR 0003423
I. Gelfand and D. Raikov, Irreducible unitary representations of locally bicompact groups, C. R. (Doklady) Acad. Sci. URSS (N.S.) 42 (1944), 199–201. MR 0011307
I. Gelfand and G. Šilov, Über verschiedene Methoden der Einführung der Topologie in die Menge der maximalen Ideale eines normierten Ringes, Rec. Math. [Mat. Sbornik] N.S. 9 (51) (1941), 25–39 (German, with Russian summary). MR 0004729

On Laplace integrals

Einar Hille and J. D. Tamarkin, On the characteristic values of linear integral equations, Acta Math. 57 (1931), no. 1, 1–76. MR 1555331, DOI 10.1007/BF02403043

Questions of relative inclusion in the domain of Hausdorff means

On moment functions

On the theory of Laplace integrals

N. H. McCoy and Deane Montgomery, A representation of generalized Boolean rings, Duke Math. J. 3 (1937), no. 3, 455–459. MR 1546001, DOI 10.1215/S0012-7094-37-00335-1
F. J. Murray and J. Von Neumann, On rings of operators, Ann. of Math. (2) 37 (1936), no. 1, 116–229. MR 1503275, DOI 10.2307/1968693
F. J. Murray and J. von Neumann, On rings of operators. IV, Ann. of Math. (2) 44 (1943), 716–808. MR 9096, DOI 10.2307/1969107
J. v. Neumann, Almost periodic functions in a group. I, Trans. Amer. Math. Soc. 36 (1934), no. 3, 445–492. MR 1501752, DOI 10.1090/S0002-9947-1934-1501752-3
F. Peter and H. Weyl, Die Vollständigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe, Math. Ann. 97 (1927), no. 1, 737–755 (German). MR 1512386, DOI 10.1007/BF01447892
H. R. Pitt, General Tauberian theorems. II, J. London Math. Soc. 15 (1940), 97–112. MR 2649, DOI 10.1112/jlms/s1-15.2.97
N. Wiener and H. R. Pitt, On absolutely convergent Fourier-Stieltjes transforms, Duke Math. J. 4 (1938), no. 2, 420–436. MR 1546064, DOI 10.1215/S0012-7094-38-00435-1
I. E. Segal, The group ring of a locally compact group. I, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 348–352. MR 4633, DOI 10.1073/pnas.27.7.348
I. E. Segal, The span of the translations of a function in a Lebesgue space, Proc. Nat. Acad. Sci. U.S.A. 30 (1944), 165–169. MR 10642, DOI 10.1073/pnas.30.7.165

Sur les espaces des fonctions presque périodiques

M. H. Stone, The theory of representations for Boolean algebras, Trans. Amer. Math. Soc. 40 (1936), no. 1, 37–111. MR 1501865, DOI 10.1090/S0002-9947-1936-1501865-8
M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), no. 3, 375–481. MR 1501905, DOI 10.1090/S0002-9947-1937-1501905-7

l’Integration dans les groupes topologiques et ses applications

Norbert Wiener, Tauberian theorems, Ann. of Math. (2) 33 (1932), no. 1, 1–100. MR 1503035, DOI 10.2307/1968102

The Fourier integral and certain of its applications