scholarly journals The inverse of banded matrices

2013 ◽  
Vol 237 (1) ◽  
pp. 126-135 ◽  
Author(s):  
Emrah Kılıç ◽  
Pantelimon Stanica
Keyword(s):  
2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Muhammed Altun

The fine spectra of upper and lower triangular banded matrices were examined by several authors. Here we determine the fine spectra of tridiagonal symmetric infinite matrices and also give the explicit form of the resolvent operator for the sequence spaces , , , and .


Author(s):  
Mahamet Koïta ◽  
Stanislas Kupin ◽  
Sergey Naboko ◽  
Belco Touré

Abstract Let $L^2({{\mathbb{D}}})$ be the space of measurable square-summable functions on the unit disk. Let $L^2_a({{\mathbb{D}}})$ be the Bergman space, that is, the (closed) subspace of analytic functions in $L^2({{\mathbb{D}}})$. $P_+$ stays for the orthogonal projection going from $L^2({{\mathbb{D}}})$ to $L^2_a({{\mathbb{D}}})$. For a function $\varphi \in L^\infty ({{\mathbb{D}}})$, the Toeplitz operator $T_\varphi : L^2_a({{\mathbb{D}}})\to L^2_a({{\mathbb{D}}})$ is defined as $$\begin{align*} & T_\varphi f=P_+\varphi f, \quad f\in L^2_a({{\mathbb{D}}}). \end{align*}$$The main result of this article are spectral asymptotics for singular (or eigen-) values of compact Toeplitz operators with logarithmically decaying symbols, that is, $$\begin{align*} & \varphi(z)=\varphi_1(e^{i\theta})\, (1+\log(1/(1-r)))^{-\gamma},\quad \gamma>0, \end{align*}$$where $z=re^{i\theta }$ and $\varphi _1$ is a continuous (or piece-wise continuous) function on the unit circle. The result is applied to the spectral analysis of banded (including Jacobi) matrices.


2020 ◽  
Vol 18 (1) ◽  
pp. 1227-1229
Author(s):  
Yerlan Amanbek ◽  
Zhibin Du ◽  
Yogi Erlangga ◽  
Carlos M. da Fonseca ◽  
Bakytzhan Kurmanbek ◽  
...  

Abstract In this short note, we provide a brief proof for a recent determinantal formula involving a particular family of banded matrices.


1988 ◽  
Vol 4 (1) ◽  
pp. 403-417 ◽  
Author(s):  
Jeffrey S. Geronimo ◽  
Evans M. Harrell ◽  
Walter Van Assche

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