Some applications of a matrix criterion for equidistribution
Sbornik. Mathematics, Tome 192 (2001) no. 12, pp. 1877-1887 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Formulations and simple proofs of Szego-type theorems on the distribution of the eigenvalues and the singular values are given for matrices that can be obtained from a fixed finite set of Toeplitz matrices with generating functions in $L_1$ by means of a fixed finite sequence of operations of addition, multiplication, and inversion.
@article{SM_2001_192_12_a4,
     author = {E. E. Tyrtyshnikov},
     title = {Some applications of a~matrix criterion for equidistribution},
     journal = {Sbornik. Mathematics},
     pages = {1877--1887},
     year = {2001},
     volume = {192},
     number = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_12_a4/}
}
TY  - JOUR
AU  - E. E. Tyrtyshnikov
TI  - Some applications of a matrix criterion for equidistribution
JO  - Sbornik. Mathematics
PY  - 2001
SP  - 1877
EP  - 1887
VL  - 192
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/SM_2001_192_12_a4/
LA  - en
ID  - SM_2001_192_12_a4
ER  - 
%0 Journal Article
%A E. E. Tyrtyshnikov
%T Some applications of a matrix criterion for equidistribution
%J Sbornik. Mathematics
%D 2001
%P 1877-1887
%V 192
%N 12
%U http://geodesic.mathdoc.fr/item/SM_2001_192_12_a4/
%G en
%F SM_2001_192_12_a4
E. E. Tyrtyshnikov. Some applications of a matrix criterion for equidistribution. Sbornik. Mathematics, Tome 192 (2001) no. 12, pp. 1877-1887. http://geodesic.mathdoc.fr/item/SM_2001_192_12_a4/

[1] 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

[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. RAN, 333:3 (1993), 300–303 | MR | Zbl

[4] Zamarashkin N. L., Tyrtyshnikov E. E., “Raspredelenie sobstvennykh i singulyarnykh chisel teplitsevykh matrits pri oslablennykh trebovaniyakh k proizvodyaschei funktsii”, Matem. sb., 188:8 (1997), 83–92 | MR | Zbl

[5] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov, Nauka, M., 1965

[6] Grenander U., Sege G., Teplitsevy formy i ikh prilozheniya, IL, M., 1961

[7] 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

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

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

[10] Chan R., “Circulant preconditioners for Hermitian Toeplitz systems”, SIAM J. Matrix Anal. Appl., 10 (1989), 542–550 | DOI | MR | Zbl

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