Infinite Real Symmetric Toeplitz Matrix Reference - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-18T22:19:41Z http://mathoverflow.net/feeds/question/114800 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/114800/infinite-real-symmetric-toeplitz-matrix-reference Infinite Real Symmetric Toeplitz Matrix Reference Keaton Hamm 2012-11-28T18:26:48Z 2012-11-28T20:20:43Z <p>I am looking for a good starting point (book or articles) for studying Toeplitz matrices. Specifically as mentioned in the title, I am most interested in the case where they are of the form $$A = {\phi(i-j)}_{i,j\in\mathbb{Z}}$$ where $\phi:\mathbb{R}\to\mathbb{R}$ and $\phi(i-j)=\phi(j-i)$.</p> <p>I so far have looked at "Analysis of Toeplitz Operators" by Bottcher and Silbermann, but wonder if there might be some more references that address my specific interest, and if anything can be said about the explicit form of the inverse.</p> <p>I apologize if this has been answered before, but I did not find much in searching old posts.</p> http://mathoverflow.net/questions/114800/infinite-real-symmetric-toeplitz-matrix-reference/114811#114811 Answer by Bazin for Infinite Real Symmetric Toeplitz Matrix Reference Bazin 2012-11-28T20:20:43Z 2012-11-28T20:20:43Z <p>I strongly recommend the following book</p> <p>Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators Lloyd N. Trefethen &amp; Mark Embree</p> <p>The first chapter is partly devoted to Toeplitz matrices, although their interest is focused on the non-selfadjoint case. Anyhow, the book is pleasant to read and very informative.</p>