Literature Cited
U. Grenander and G. Szegö, Toeplitz Forms and Their Applications, University of California Press, Berkeley (1958).
A. Devinatz, “The strong Szegö limit theorem,” Ill. J. Math.,7, No. 1, 160–175 (1967).
H. Widom, “Asymptotic behavior of block Toeplitz matrices and determinants,” Adv. Math.,21, No. 1, 1–29 (1976).
J. Schulz and B. Silbermann, Das Asymptotische Verhalten von Toeplitz-Determinanten, Wiss. Schriftenreihe der TH Karl-Marx-Stadt (1980).
E. Basor and J. W. Helton, “A new proof of the Szegö limit theorem and new results for Toeplitz operators with discontinuous symbol,” J. Operator Theory,3 23–40 (1980).
Ya. L. Geronimus, “On a problem of G. Szegö, M. Kac, H. Baxter, and J. Hirschman,” Izv. Akad. Nauk SSSR, Ser. Mat.,31, No. 2, 289–304 (1967).
A. Böttcher and B. Silbermann, “Notes on the asymptotic behavior of block Toeplitz matrices and determinants,” Math. Nachr.,98, 183–210 (1980).
I. Yu. Linnik, “The multidimensional analog of G. Szegö's limit theorem,” Izv. Akad. Nauk SSSR, Ser. Mat.,39, No. 6, 1393–1403 (1975).
H. Widom, “A theorem on translation kernels in n-dimensions,” Trans. Am. Math. Soc.,94, No. 1, 170–180 (1960).
H. Widom, “Asymptotic inversion of convolution operators,” Publ. Math. I.H.E.S.,44, 191–240, (1975).
H. Widom, “Szegö's limit theorem: the higher-dimensional matrix case,” J. Funct. Anal.,39, No. 2, 182–198 (1980).
I. C. Gohberg and M. G. Krein, Introduction to the Theory Linear Nonselfadjoint Operators, Am. Math. Soc. (1969).
A. V. Kozak and I. B. Simonenko, “Projection methods for the solution of multidimensional discrete convolution equations,” Sib. Mat. Zh.,21, No. 2, 119–127 (1980).
A. V. Kozak, “The local principle in the theory of projection methods,” Dokl. Akad. Nauk SSSR,212, No. 6, 1287–1289 (1973).
A. V. Kozak, “Projection methods for the solution of multidimensional equations of convolution type,” Candidate's Dissertation, Rostov-on-Don (1974).
R. Ya. Doktorskii “On G. Szegö's limit theorem in the multidimensional case,” Funkts. Anal. Prilozhen,18, No. 1 72–73 (1984).
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Rostov-on-Don. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 25, No. 5, pp. 20–29, September–October, 1984.
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Doktorskii, R.Y. Generalization of G. Szegö's limit theorem to the multidimensional case. Sib Math J 25, 701–710 (1984). https://doi.org/10.1007/BF00968682
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DOI: https://doi.org/10.1007/BF00968682