Geodesic
On the canonical distribution of a~class of Toeplitz operators on a~locally compact Abelian group
Izvestiya. Mathematics , Tome 10 (1976) no. 5, pp. 1133-1142.

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In this paper we obtain necessary and sufficient conditions for the class of Toeplitz operators associated with Hermitian matrix-valued summable functions on a locally compact Abelian group to have canonical distribution equal to the Haar measure. Bibliography: 8 titles. 
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I. Yu. Linnik. On the canonical distribution of a~class of Toeplitz operators on a~locally compact Abelian group. Izvestiya. Mathematics , Tome 10 (1976) no. 5, pp. 1133-1142. http://geodesic.mathdoc.fr/item/IM2_1976_10_5_a9/

[1] Grenander U., Segë G., Tëplitsevy formy i ikh prilozheniya, IIL, M., 1961

[2] Krieger H. A.,, “Toeplitz operators on locally compact abelian groups”, J. Math. and Mech., 14:3 (1965), 439–478 | MR | Zbl

[3] Sacrison D. J., “An extension of the theorem Kac, Murdock and Szegö to $N$-dimensions”, IEEE, Trans. Inform. Theory, 15:5 (1969), 608–610 | DOI | MR

[4] Barladyan B. Kh., “Obobschenie teoremy Katsa, Merdoka i Segë na $N$-mernoe prostranstvo”, Problemy peredachi informatsii, 10:3 (1974), 62–69 | MR | Zbl

[5] Ryuel D., Statisticheskaya mekhanika. Strogie rezultaty, Mir, M., 1971

[6] Riss F., Sekefalvi-Nad B., Lektsii po funktsionalnomu analizu, IIL, M., 1954

[7] Linnik I. Yu., “Prostranstvennoe obobschenie odnoi teoremy o tëplitsevom operatore”, Matematicheskie zametki, 14:6 (1973), 895–900 | MR | Zbl

[8] Linnik I. Yu., “Prostranstvennoe obobschenie teoremy M. Katsa ob opredelitele tëplitseva operatora”, Dokl. AN SSSR, 217:5 (1974), 2011–2012 | MR