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Sequences of variable-coefficient Toeplitz matrices and their singular values.
- Source :
-
Journal of Functional Analysis . Feb2016, Vol. 270 Issue 4, p1479-1500. 22p. - Publication Year :
- 2016
-
Abstract
- The purpose of this paper is to describe asymptotic spectral properties of sequences of variable-coefficient Toeplitz matrices. These sequences, A N ( a ) , with a being in a Wiener type algebra and defined on an annular cylinder ( [ 0 , 1 ] 2 × T ) , widely generalize the sequences of finite sections of a Toeplitz operator. We prove that if a ( x , x , t ) does not vanish for every ( x , t ) ∈ [ 0 , 1 ] × T then the singular values of A N ( a ) have the k -splitting property, which means that, there exists an integer k such that, for N large enough, the first k -singular values of A N ( a ) converge to zero as N → ∞ , while the others are bounded away from zero, with k = dim ker T ( a ( 0 , 0 , t ) ) + dim ker T ( a ( 1 , 1 , t − 1 ) ) , the sum of the kernel dimensions of two Toeplitz operators. In the end of the paper we discuss Fredholm properties of the mentioned sequences and describe them completely. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00221236
- Volume :
- 270
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Journal of Functional Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 112264068
- Full Text :
- https://doi.org/10.1016/j.jfa.2015.11.012