The toeplitz-operators tag has no usage guidance.

**6**

votes

**0**answers

58 views

### Quantitive strong Szegő limit theorem

Background: Let $\varphi: \mathbb{T} \to \mathbb{C}$ be a complex function on the unit circle admitting a Fourier expansion. Denote its Fourier coefficients by $\widehat{\varphi}_k$: ...

**1**

vote

**0**answers

63 views

### On triangular Toeplitz matrices

Let $R(x)$ be the upper triangular Toeplitz matrix with first row $x$, so that $R_{ik}=x_{k-i+1}$ if $i\le k$ and $R_{ik}=0$ otherwise. Let $N(n)$ be the smallest number $N$ such that there exist ...

**3**

votes

**0**answers

39 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

**5**answers

458 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

**1**answer

109 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

**0**answers

217 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

**1**answer

249 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

**1**answer

834 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

**0**answers

237 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

**0**answers

395 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

**2**answers

345 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 ...