Geodesic
Schatten norms of Toeplitz matrices with Fisher--Hartwig singularities
The electronic journal of linear algebra, Tome 15 (2006), pp. 251-259.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The asymptotics of the Schatten norms of finite Toeplitz matrices generated by functions with a Fisher-Hartwig singularity are described as the matrix dimension n goes to infinity. The message of the paper is to reveal some kind of a kink: the pth Schatten norm increases as n to the power 1/p before the singularity reaches a critical point and as n to an exponent depending on the singularity beyond the critical point.
Classification : 47B35, 15A60
Keywords: Toeplitz matrix, schatten norm, Fisher-hartwig singularity, avram-parter theorem, Szego theorem 
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     author = {B\"ottcher, Albrecht},
     title = {Schatten norms of {Toeplitz} matrices with {Fisher--Hartwig} singularities},
     journal = {The electronic journal of linear algebra},
     pages = {251--259},
     publisher = {mathdoc},
     volume = {15},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2006__15__a8/}
}
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Böttcher, Albrecht. Schatten norms of Toeplitz matrices with Fisher--Hartwig singularities. The electronic journal of linear algebra, Tome 15 (2006), pp. 251-259. http://geodesic.mathdoc.fr/item/ELA_2006__15__a8/