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Spectral theory for semi-groups of linear operators. (English) Zbl 0045.21502


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[1] Warren Ambrose, Spectral resolution of groups of unitary operators, Duke Math. J. 11 (1944), 589 – 595. · Zbl 0061.25409
[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. · JFM 65.0483.02
[3] I. Gelfand, Normierte Ringe, Rec. Math. [Mat. Sbornik] N. S. 9 (51) (1941), 3 – 24 (German, with Russian summary). · JFM 67.0406.02
[4] I. Gelfand, Zur Theorie der Charaktere der Abelschen topologischen Gruppen, Rec. Math. [Mat. Sbornik] N. S. 9 (51) (1941), 49 – 50 (German, with Russian summary). · JFM 67.0407.02
[5] I. Gelfand, Über absolut konvergente trigonometrische Reihen und Integrale, Rec. Math. [Mat. Sbornik] N. S. 9 (51) (1941), 51 – 66 (German, with Russian summary). · JFM 67.0409.03
[6] Einar Hille, Functional Analysis and Semi-Groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, New York, 1948. · Zbl 0033.06501
[7] Einar Hille, On the differentiability of semi-group operators, Acta Sci. Math. Szeged 12 (1950), no. Leopoldo Fejér et Frederico Riesz LXX annos natis dedicatus, Pars B, 19 – 24. · Zbl 0035.35802
[8] B. v. Sz. Nagy, Spektraldarstellung linearer Transformationen des Hilbertschen Raumes, Ergebnisse der Mathematik, vol. 5, Berlin, 1942. · JFM 68.0241.01
[9] M. Neumark, Positive definite operator functions on a commutative group, Bull. Acad. Sci. URSS Sér. Math. [Izvestia Akad. Nauk SSSR] 7 (1943), 237 – 244 (Russian, with English summary). · Zbl 0061.25411
[10] R. S. Phillips, On semi-groups of operators, Proceedings of the American Mathematical Society vol. 2 (1951) pp. 234-237. · Zbl 0043.11404
[11] M. H. Stone, On one-parameter unitary groups in Hilbert space, Ann. of Math. (2) 33 (1932), no. 3, 643 – 648. · Zbl 0005.16403 · doi:10.2307/1968538
[12] M. H. Stone, A general theory of spectra. I, Proc. Nat. Acad. Sci. U. S. A. 26 (1940), 280 – 283. · Zbl 0063.07208
[13] M. H. Stone, A general theory of spectra. II, Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 83 – 87. · Zbl 0063.07209
[14] M. H. Stone, Boundedness properties in function-lattices, Canadian J. Math. 1 (1949), 176 – 186. · Zbl 0032.16901
[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.) 30 (1941), 785 – 787 (French). · Zbl 0024.41403
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