Literature Cited
M. Sato, T. Miwa, and M. Jimbo, “Holonomic quantum fields. V.,” Publ. RIMS, Kyoto Univ.,16, 531 (1980).
I. A. Ibragimov and Yu. A. Rozanov, Gaussian Random Processes [in Russian], Nauka, Moscow (1970).
R. L. Dobrushin, “Gaussian random fields — Gibbsian point of view,” in: Multicomponent Random Systems, Marcel Dekker, New York (1980), pp. 119–151.
L. Carleson, “Some analytic problems related to statistical mechanics,” Lect. Notes. Math.,779, 5 (1980).
B. M. McCoy and T. T. Wu, “Theory of Toeplitz determinants and the spin correlations of the two-dimensional Ising modes. IV,” Phys. Rev.,162, 436 (1967).
M. Fisher, “Theory of singularities at a critical point,” in: Stability and Phase Transitions [Russian translations], Mir, Moscow (1973), pp. 245–369.
A. J. Bray and M. A. Moore, “Critical behavior of semi-infinite systems,” J. Phys. A,10, 1927 (1977).
U. Grenander and G. Szegö, Toeplitz Forms and their Applications, Berkeley (1958).
D. Ruelle, Statistical Mechanics, New York (1969).
F. J. Dyson, “Existence of a phase transition in a one-dimensional Ising ferromagnet,” Commun. Math. Phys.,12, 91 (1969).
V. S. Vladimirov, Generalized Functions in Mathematical Physics [in Russian], Nauka, Moscow (1979).
I. A. Ibragimov, “On a theorem of Szegö,” Matem. Zametki,3, 693 (1968).
Constructive Quantum Field Theory (eds. G. Velo and A. Wightman) (Lecture Notes in Physics, Vol. 25), Springer, New York (1973).
G. Baxter and I. I. Hirschman (Jr), “An explicit inversion formula for finite-section Wiener-Hopf operators,” Bull. Am. Math. Soc.,70, 820 (1964).
I. Ts. Gokhberg and A. A. Sementsul, “Inversion of finite Toeplitz matrices and their continuous analogs,” Matem. Issled. (Kishinev),7, 201 (1972).
M. G. Krein, “Integral equations on a half-line with kernels that depend on the difference of arguments,” Usp. Mat. Nauk,13, 3 (1958).
M. A. Naimark, Normed Rings, Groningen (1960).
W. Rudin, Function Theory in Polydisks, New York (1969).
I. I. Danilyuk, Irregular Boundary-Value Problems on the Plane [in Russian], Nauka, Moscow (1975).
G. Baxter, “A norm inequality for a “finite-section” Wiener-Hopf equation,” Illinois J. Math.,7, 97 (1963).
G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge (1952).
T. T. Wu, “Theory of Toeplitz determinants and of the spin correlations of the two-dimensional Ising model,” Phys. Rev.,149, 380 (1966).
M. Kac, in: Summer Institute on Spectral Theory and Statistical Mechanics (ed. J. D. Pincus), Brookhaven Natl. Lab. Rept. BNL 993 (T-422) (1966).
M. E. Fisher and R. E. Hartwig, “Toeplitz determinants: Some applications, theorems, and conjectures,” Adv. Chem. Phys.,15, 333 (1969).
R. E. Hartwig and M. E. Fisher, “Asymptotic behavior of Toeplitz matrices and determinants,” Arch. Ration. Mech. Anal.,32, 190 (1969).
P. M. Blekher, “Inversion of Toeplitz matrices,” Tr. MMO,40, 207 (1979).
L. Bieberbach, Analytische Fortsetzung, Berlin (1955).
V. S. Vladimirov, Yu. N. Drozhzhinov, and B. I. Zav'yalov, “Tauberian theorems for generalized functions,” Tr. Mosk. Inst. Akad. Nauk SSSR,163 (1982).
I. Yu. Linnik, Izv. Akad. Nauk SSSR, Ser. Mat.,39, 1393 (1975).
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V. A. Steklov Mathematics Institute, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 54, No. 1, pp. 8–22, January, 1983.
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Vladimirov, V.S., Volovich, I.V. A statistical physics model. Theor Math Phys 54, 1–12 (1983). https://doi.org/10.1007/BF01017118
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DOI: https://doi.org/10.1007/BF01017118