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3
votes
0answers
36 views

Is there a possibility to find the toeplitz matrix that has the nearest column space to a given matrix?

As is said, if we have a known matrix $D \in \mathbb{R}^{N \times k}$ with $k<N$, is there a way that we can find a toeplitz matrix $D_T \in \mathbb{R}^{N \times k}$, which satisfies $$ ...
6
votes
5answers
406 views

The maximal eigenvalue of a symmetric Toeplitz matrix

Let $0\le x\le 1$ be a real number. Denote by $A_n(x)=(a_{ij})$ the $n$ by $n$ matrix such that $a_{ij}=x^{|i-j|}$ and let $\lambda_n(x)$ be the maximal eigenvalue of $A_n(x)$. Is there any ...
1
vote
1answer
106 views

Infinite Real Symmetric Toeplitz Matrix Reference

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 = ...
0
votes
0answers
216 views

L1-regularized Least Squares on a matrix with Toeplitz Blocks (not block-Toeplitz)

I am trying to speed up a sparse signal recovery algorithms. My sensing matrix is a set of Toeplitz Blocks, M = [T1,T2,T3,...,Tk] The objective is min ||Mx - b||_2^2 + ||x||1 What I'm actually ...
1
vote
1answer
242 views

Invertibility of frame/sampling operator on Bargmann-Fock spaces

Let $F_\alpha ^p (\mathbb{C}^n)$ for $1 < p < \infty$ and $\alpha > 0$ be the Bargmann-Fock space defined as the Banach space of entire functions $f$ such that $f(\cdot) e^{- \frac{\alpha}{2} ...
4
votes
1answer
804 views

annihilator/common left multiple of matrix polynomials

Let $A_{n,d}$ be the space of polynomials of degree $d$ or less whose coefficients are real $n\times n$ matrices --- or, if you prefer, the space of matrices whose entries are degree-$d$ polynomials. ...
4
votes
0answers
236 views

Can one pose a Toeplitz index problem associated to a discrete group?

Before posing my question, let me provide a little background since the Wikipedia page on this stuff is sorely lacking. Let's start with the classical case of the Toeplitz index problem on the ...
5
votes
0answers
393 views

Convolutions and Toeplitz Operators

Let be $d>0$ an integer number and consider the Cartesian product $\mathbb Z^d$ as metric space, with the distance between $x,y\in\mathbb Z^d$ given by $\|x-y\|_1=\sum_{j=0}^d|x_j-y_j|$. Let be ...
7
votes
2answers
341 views

Where can I learn about (the asymptotics of) Toeplitz operators?

Toeplitz operators provide a natural language with which to do geometric quantization. I don't want to really understand them, and I don't need them in full generality. I'm looking for some ...