Geodesic
Distribution of eigenvalues and singular values of Toeplitz matrices under weakened conditions on the generating function
Sbornik. Mathematics, Tome 188 (1997) no. 8, pp. 1191-1201 
N. L. Zamarashkin; E. E. Tyrtyshnikov. Distribution of eigenvalues and singular values of Toeplitz matrices under weakened conditions on the generating function. Sbornik. Mathematics, Tome 188 (1997) no. 8, pp. 1191-1201. http://geodesic.mathdoc.fr/item/SM_1997_188_8_a5/
@article{SM_1997_188_8_a5,
     author = {N. L. Zamarashkin and E. E. Tyrtyshnikov},
     title = {Distribution of eigenvalues and singular values of {Toeplitz} matrices under weakened conditions on the~generating function},
     journal = {Sbornik. Mathematics},
     pages = {1191--1201},
     year = {1997},
     volume = {188},
     number = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_8_a5/}
}
TY  - JOUR
AU  - N. L. Zamarashkin
AU  - E. E. Tyrtyshnikov
TI  - Distribution of eigenvalues and singular values of Toeplitz matrices under weakened conditions on the generating function
JO  - Sbornik. Mathematics
PY  - 1997
SP  - 1191
EP  - 1201
VL  - 188
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/SM_1997_188_8_a5/
LA  - en
ID  - SM_1997_188_8_a5
ER  - 
%0 Journal Article
%A N. L. Zamarashkin
%A E. E. Tyrtyshnikov
%T Distribution of eigenvalues and singular values of Toeplitz matrices under weakened conditions on the generating function
%J Sbornik. Mathematics
%D 1997
%P 1191-1201
%V 188
%N 8
%U http://geodesic.mathdoc.fr/item/SM_1997_188_8_a5/
%G en
%F SM_1997_188_8_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

A new approach to the study of asymptotic distributions of eigenvalues and singular values of Toeplitz matrices is presented; this approach involves a matrix criterion for equidistribution. Theorems of Szego type for generating functions in $L_1$ are obtained.

[1] Grenander V., Szego G., Toeplitz Forms and Their Applications, Univ. of California Press, Berkeley, 1958 | MR | Zbl

[2] Tyrtyshnikov E. E., “Raspredeleniya i klastery”, Matrichnye metody i algoritmy, IVM RAN, M., 1993, 124–166 | MR

[3] Tyrtyshnikov E. E., “Novye teoremy o raspredelenii sobstvennykh i singulyarnykh chisel mnogourovnevykh teplitsevykh matrits”, Dokl. AN, 333:3 (1993), 300–303 | MR

[4] Tyrtyshnikov E. E., “A unifying approach to some old and new theorems on distribution and clustering”, Linear Algebra Appl., 232 (1996), 1–43 | DOI | MR | Zbl

[5] Avram F., “On bilinear forms on Gaussian random variables and Toeplitz matrices”, Probab. Theory Related Fields, 79 (1988), 37–45 | DOI | MR | Zbl

[6] Parter S. V., “On the distribution of the singular values of Toeplitz matrices”, Linear Algebra Appl., 80 (1986), 115–130 | DOI | MR | Zbl

[7] Tyrtyshnikov E. E., “Influence of matrix operations on the distribution of eigenvalues and singular values of Toeplitz matrices”, Linear Algebra Appl., 207 (1994), 225–249 | DOI | MR | Zbl

[8] Kolmogorov A. N., “O poryadke ubyvaniya koeffitsientov ryada Fure–Lebega”, Izbrannye trudy. Matematika i mekhanika, Nauka, M., 1985, 12–14 | MR

[9] Tyrtyshnikov E. E., Teplitsevy matritsy, nekotorye ikh analogi i prilozheniya, OVM AN SSSR, M., 1989 | MR