Finite and Infinite Gap Jacobi Matrices

2012 ◽  
pp. 43-55
Author(s):  
Jacob S. Christiansen
Keyword(s):  
Jacobi Matrices

Inverse problems for finite Jacobi matrices and Krein–Stieltjes strings

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alexander Mikhaylov ◽  
Victor Mikhaylov
Keyword(s):  
Dynamical System ◽  
Inverse Problems ◽  
Jacobi Matrix ◽  
Jacobi Matrices ◽  
Unknown Parameters ◽  
Stieltjes String ◽  
Propagation Of Waves ◽  
Dynamic Inverse

Abstract We consider dynamic inverse problems for a dynamical system associated with a finite Jacobi matrix and for a system describing propagation of waves in a finite Krein–Stieltjes string. We offer three methods of recovering unknown parameters: entries of a Jacobi matrix in the first problem and point masses and distances between them in the second, from dynamic Dirichlet-to-Neumann operators. We also answer a question on a characterization of dynamic inverse data for these two problems.

scholarly journals An inverse eigenvalue problem for modified pseudo-Jacobi matrices

2021 ◽  
Vol 389 ◽  
pp. 113361
Author(s):  
Wei-Ru Xu ◽  
Natália Bebiano ◽  
Guo-Liang Chen
Keyword(s):  
Eigenvalue Problem ◽  
Inverse Eigenvalue Problem ◽  
Jacobi Matrices ◽  
Inverse Eigenvalue

scholarly journals Remarks on periodic Jacobi matrices on trees

2021 ◽  
Vol 62 (4) ◽  
pp. 042101
Author(s):  
Jacob S. Christiansen ◽  
Barry Simon ◽  
Maxim Zinchenko
Keyword(s):  
Jacobi Matrices

scholarly journals Upper Bounds On Wavepacket Spreading For Random Jacobi Matrices

2007 ◽  
Vol 273 (3) ◽  
pp. 601-618 ◽  
Author(s):  
Svetlana Jitomirskaya ◽  
Hermann Schulz-Baldes
Keyword(s):  
Upper Bounds ◽  
Jacobi Matrices ◽  
Random Jacobi Matrices

scholarly journals On Spectral Properties of Compact Toeplitz Operators on Bergman Space with Logarithmically Decaying Symbol and Applications to Banded Matrices

2021 ◽  
Author(s):  
Mahamet Koïta ◽  
Stanislas Kupin ◽  
Sergey Naboko ◽  
Belco Touré
Keyword(s):  
Spectral Analysis ◽  
Continuous Function ◽  
Bergman Space ◽  
Orthogonal Projection ◽  
Spectral Properties ◽  
Toeplitz Operators ◽  
Closed Subspace ◽  
Jacobi Matrices ◽  
Banded Matrices ◽  
Eigen Values

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.

scholarly journals The Jacobi matrices approach to Nevanlinna–Pick problems

2011 ◽  
Vol 163 (2) ◽  
pp. 117-142 ◽  
Author(s):  
Maxim Derevyagin
Keyword(s):  
Jacobi Matrices
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