Accessibility navigation


Singular values of multiplicative Toeplitz matrices

Hilberdink, T. (2017) Singular values of multiplicative Toeplitz matrices. Linear and Multilinear Algebra, 65 (4). pp. 813-829. ISSN 1563-5139

[img]
Preview
Text - Accepted Version
· Please see our End User Agreement before downloading.

418kB

It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

To link to this item DOI: 10.1080/03081087.2016.1204978

Abstract/Summary

We study the asymptotic behaviour of the singular values of matrices with entries $a_{ij}=f(i/j)$ if $j|i$ and zero otherwise, with $f$ an arithmetical function. In particular, we study the case where $f$ is multiplicative and $F(x):=\sum_{n\leq x} |f(n)|^2$ is regularly varying. Our main result is that, under quite general conditions, the singular values are, asymptotically, $\sqrt{\mu_r F(n)}$, where $\{\mu_r:r=1,2,3,\ldots\}$ are the eigenvalues of some positive Hilbert-Schmidt operator.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:66059
Publisher:Taylor & Francis

Downloads

Downloads per month over past year

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation