{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T22:33:28Z","timestamp":1777761208104,"version":"3.51.4"},"reference-count":23,"publisher":"Emerald","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,10,15]]},"abstract":"<jats:p>The present monograph studies the asymptotic behaviour of eigenvalues, products and functions of block Toeplitz matrices generated by the Fourier coefficients of a continuous matrix-valued function. This study is based on the concept of asymptotically equivalent sequences of non-square matrices. The asymptotic results on block Toeplitz matrices obtained are applied to vector asymptotically wide sense stationary processes. Therefore, this monograph is a generalization to block Toeplitz matrices of the Gray monograph entitled \u201cToeplitz and circulant matrices: A review\u201d, which was published in the second volume of Foundations and Trends in Communications and Information Theory, and which is the simplest and most famous introduction to the asymptotic theory on Toeplitz matrices.<\/jats:p>","DOI":"10.1561\/0100000066","type":"journal-article","created":{"date-parts":[[2012,10,15]],"date-time":"2012-10-15T13:23:13Z","timestamp":1350307393000},"page":"179-257","source":"Crossref","is-referenced-by-count":44,"title":["Block Toeplitz Matrices: Asymptotic Results and Applications"],"prefix":"10.1108","volume":"8","author":[{"given":"Jes\u00fas","family":"Guti\u00e9rrez-Guti\u00e9rrez","sequence":"first","affiliation":[{"name":"CEIT and Tecnun (University of Navarra) , Manuel Lardiz\u00e1bal 15, San Sebasti\u00e1n,","place":["Spain"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pedro M.","family":"Crespo","sequence":"additional","affiliation":[{"name":"CEIT and Tecnun (University of Navarra) , Manuel Lardiz\u00e1bal 15, San Sebasti\u00e1n,","place":["Spain"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","published-online":{"date-parts":[[2012,10,15]]},"reference":[{"key":"2026032711581322200_ref001","volume-title":"Mathematical Analysis","author":"Apostol","year":"1974"},{"key":"2026032711581322200_ref002","doi-asserted-by":"crossref","DOI":"10.1515\/9781400833344","volume-title":"Matrix Mathematics: Theory, Facts, and Formulas","author":"Bernstein","year":"2009"},{"key":"2026032711581322200_ref003","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.cam.2006.04.046","article-title":"Mass concentration in quasicommutators of Toeplitz matrices","volume":"205","author":"B\u00f6ttcher","year":"2007","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"2026032711581322200_ref004","volume-title":"Elementary Differential Equations and Boundary Value Problems","author":"Boyce","year":"2005"},{"issue":"3","key":"2026032711581322200_ref005","doi-asserted-by":"crossref","first-page":"1168","DOI":"10.1109\/TIT.2006.890697","article-title":"On the elementwise convergence of continuous functions of Hermitian banded Toeplitz matrices","volume":"53","author":"Crespo","year":"2007","journal-title":"IEEE Transactions on Information Theory"},{"issue":"3","key":"2026032711581322200_ref006","doi-asserted-by":"crossref","first-page":"1243","DOI":"10.1109\/18.915697","article-title":"Asymptotic eigenvalue distribution of block Toeplitz matrices and application to blind SIMO channel identification","volume":"47","author":"Gazzah","year":"2001","journal-title":"IEEE Transactions on Information Theory"},{"issue":"6","key":"2026032711581322200_ref007","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1109\/TIT.1972.1054924","article-title":"On the asymptotic eigenvalue distribution of Toeplitz matrices","volume":"IT-18","author":"Gray","year":"1972","journal-title":"IEEE Transactions on Information Theory"},{"issue":"3","key":"2026032711581322200_ref008","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1561\/0100000006","article-title":"Toeplitz and circulant matrices: A review","volume":"2","author":"Gray","year":"2006","journal-title":"Foundations and Trends in Communications and Information Theory"},{"key":"2026032711581322200_ref009","volume-title":"Toeplitz Forms and their Applications","author":"Grenander","year":"1984"},{"key":"2026032711581322200_ref010","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.amc.2008.01.022","article-title":"Positive integer powers of certain tridiagonal matrices","volume":"202","author":"Guti\u00b4errez-Guti\u00b4errez","year":"2008","journal-title":"Applied Mathematics and Computation"},{"key":"2026032711581322200_ref011","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1016\/j.amc.2008.10.005","article-title":"Powers of tridiagonal matrices with constant diagonals","volume":"206","author":"Guti\u00b4errez-Guti\u00b4errez","year":"2008","journal-title":"Applied Mathematics and Computation"},{"issue":"12","key":"2026032711581322200_ref012","doi-asserted-by":"crossref","first-page":"5671","DOI":"10.1109\/TIT.2008.2006401","article-title":"Asymptotically equivalent sequences of matrices and Hermitian block Toeplitz matrices with continuous symbols: Applications to MIMO systems","volume":"54","author":"Guti\u00b4errez-Guti\u00b4errez","year":"2008","journal-title":"IEEE Transactions on Information Theory"},{"issue":"8","key":"2026032711581322200_ref013","doi-asserted-by":"crossref","first-page":"5444","DOI":"10.1109\/TIT.2011.2159042","article-title":"Asymptotically equivalent sequences of matrices and multivariate ARMA processes","volume":"57","author":"Guti\u00b4errez-Guti\u00b4errez","year":"2011","journal-title":"IEEE Transactions on Information Theory"},{"key":"2026032711581322200_ref014","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1016\/j.laa.2006.12.008","article-title":"Functions of banded Hermitian block Toeplitz matrices in signal processing","volume":"422","author":"Guti\u00b4errez-Guti\u00b4errez","year":"2007","journal-title":"Linear Algebra and its Applications"},{"key":"2026032711581322200_ref015","doi-asserted-by":"crossref","first-page":"2237","DOI":"10.1016\/j.sigpro.2011.04.001","article-title":"Geometric MMSE for one-sided and two-sided vector linear predictors: From the finite-length case to the infinite-length case","volume":"91","author":"Guti\u00b4errez-Guti\u00b4errez","year":"2011","journal-title":"Signal Processing"},{"key":"2026032711581322200_ref016","volume-title":"Topics in Matrix Analysis","author":"Horn","year":"1994"},{"key":"2026032711581322200_ref017","volume-title":"Linear Systems","author":"Kailath","year":"1980"},{"issue":"4","key":"2026032711581322200_ref018","doi-asserted-by":"crossref","first-page":"1293","DOI":"10.1109\/18.243446","article-title":"Proper complex random processes with applications to information theory","volume":"39","author":"Neeser","year":"1993","journal-title":"IEEE Transactions on Information Theory"},{"issue":"10","key":"2026032711581322200_ref019","doi-asserted-by":"crossref","first-page":"5006","DOI":"10.1109\/TSP.2010.2053360","article-title":"Detection of spatially correlated Gaussian time series","volume":"58","author":"Ram\u00edrez","year":"2010","journal-title":"IEEE Transactions on Signal Processing"},{"key":"2026032711581322200_ref020","volume-title":"Principles of Mathematical Analysis","author":"Rudin","year":"1976"},{"key":"2026032711581322200_ref021","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1080\/03081089808818584","article-title":"A note on the spectral distribution of Toeplitz matrices","volume":"45","author":"Tilli","year":"1998","journal-title":"Linear and Multilinear Algebra"},{"key":"2026032711581322200_ref022","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0024-3795(85)90277-0","article-title":"On the eigenvalue problem for Toeplitz band matrices","volume":"64","author":"Trench","year":"1985","journal-title":"Linear Algebra and its Applications"},{"issue":"4","key":"2026032711581322200_ref023","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1109\/18.32152","article-title":"The capacity region of the symbol-asynchronous Gaussian multipleaccess channel","volume":"35","author":"Verd\u00fa","year":"1989","journal-title":"IEEE Transactions on Information Theory"}],"container-title":["Foundations and Trends\u00ae in Communications and Information Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.emerald.com\/ftcit\/article-pdf\/8\/3\/179\/10977048\/0100000066en.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/www.emerald.com\/ftcit\/article-pdf\/8\/3\/179\/10977048\/0100000066en.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T14:10:47Z","timestamp":1777471847000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.emerald.com\/ftcit\/article\/8\/3\/179\/1324920\/Block-Toeplitz-Matrices-Asymptotic-Results-and"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,10,15]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,10,15]]}},"URL":"https:\/\/doi.org\/10.1561\/0100000066","relation":{},"ISSN":["1567-2190","1567-2328"],"issn-type":[{"value":"1567-2190","type":"print"},{"value":"1567-2328","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,10,15]]}}}