Geodesic
Block-Toeplitz matrices and associated properties of a~Gaussian model on a~half-axis
Teoretičeskaâ i matematičeskaâ fizika, Tome 63 (1985) no. 1, pp. 154-160

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A Gaussian model on a half-axis with interaction given by a block-Toeplitz matrix $\{s_{j-k}\}^\infty_{j,k=0}$. is studied. A procedure is indicated for calculating the correlation functions and the free energy in the absence of an external field and for several ways of including such a field. The results are formulated in terms of a matrix measure $\sigma$, whose Fourier coefficients are $s_j$. These results are based on the asymptotic behavior found in the paper for the individual blocks of the matrix $(\{s_{j-k}\}^n_{j,k=0})^{-1}$ and their sums in the limit $n\to\infty$. 
@article{TMF_1985_63_1_a10,
     author = {A. L. Sakhnovich and I. M. Spitkovsky},
     title = {Block-Toeplitz matrices and associated properties of {a~Gaussian} model on a~half-axis},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {154--160},
     publisher = {mathdoc},
     volume = {63},
     number = {1},
     year = {1985},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1985_63_1_a10/}
}
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A. L. Sakhnovich; I. M. Spitkovsky. Block-Toeplitz matrices and associated properties of a~Gaussian model on a~half-axis. Teoretičeskaâ i matematičeskaâ fizika, Tome 63 (1985) no. 1, pp. 154-160. http://geodesic.mathdoc.fr/item/TMF_1985_63_1_a10/