Browsing by Subject "eigenvalue"

Now showing 1 - 20 of 20

Access status: Open Access ,
Approximation of eigenvalues of some unbounded self-adjoint discrete Jacobi matrices by eigenvalues of finite submatrices
(2007) Malejki, Maria
We investigate the problem of approximation of eigenvalues of some self-adjoint operator in the Hilbert space $l^2(\mathbb{N})$ by eigenvalues of suitably chosen principal finite submatrices of an infinite Jacobi matrix that defines the operator considered. We assume the Jacobi operator is bounded from below with compact resolvent. In our research we estimate the asymptotics (with $n\to \infty$) of the joint error of approximation for the first n eigenvalues and eigenvectors of the operator by the eigenvalues and eigenvectors of the finite submatrix of order $n \times n$. The method applied in our research is based on the Rayleigh-Ritz method and Volkmer's results included in . We extend the method to cover a class of infinite symmetric Jacobi matrices with three diagonals satisfying some polynomial growth estimates.
Access status: Restricted ,
Aproksymacja wartości własnych macierzy nieskończonych wartościami własnymi macierzy skończonych
(Data obrony: 2009-07-14) Mazurek, Anna
Wydział Matematyki Stosowanej
Access status: Restricted ,
Aproksymacja wartości własnych nieskończonych zespolonych macierzy Jacobiego
(Data obrony: 2013-07-16) Bednarz, Tomasz
Wydział Matematyki Stosowanej
Access status: Open Access ,
Asymptotic behaviour and approximation of eigenvalues for unbounded block Jacobi matrices
(2010) Malejki, Maria
The research included in the paper concerns a class of symmetric block Jacobi matrices. The problem of the approximation of eigenvalues for a class of a self-adjoint unbounded operators is considered. We estimate the joint error of approximation for the eigenvalues, numbered from $1$ to $N$, for a Jacobi matrix $J$ by the eigenvalues of the finite submatrix $J_{n}$ of order $pn \times pn$, where $N = \max \{k \in \mathbb{N}: k \leq rpn\}$ and $r \in (0,1)$ is suitably chosen. We apply this result to obtain the asymptotics of the eigenvalues of $J$ in the case $p = 3$.
Access status: Open Access ,
Asymptotics of the discrete spectrum for complex Jacobi matrices
(2014) Malejki, Maria
The spectral properties and the asymptotic behaviour of the discrete spectrum for a special class of inﬁnite tridiagonal matrices are given. We derive the asymptotic formulae for eigenvalues of unbounded complex Jacobi matrices acting in $l^2(\mathbb{N})$.
Access status: Restricted ,
Asymptotyka widma punktowego dla blokowych macierzy Jacobiego
(Data obrony: 2018-12-17) Jaskuła, Tomasz
Wydział Matematyki Stosowanej
Access status: Open Access ,
Discrete spectra for some complex infinite band matrices
(Wydawnictwa AGH, 2021) Malejki, Maria
Under suitable assumptions the eigenvalues for an unbounded discrete operator $A$ in $l_2$, given by an infinite complex band-type matrix, are approximated by the eigenvalues of its orthogonal truncations. Let $\Lambda (A)=\{\lambda \in {\rm Lim}_{n\to \infty} \lambda _n : \lambda _n \text{ is an eigenvalue of } A_n \text{ for } n \geq 1 \},$ where ${\rm Lim}_{n\to \infty} \lambda_n$ is the set of all limit points of the sequence $(\lambda_{n})$ and $A_n$ is a finite dimensional orthogonal truncation of $A$. The aim of this article is to provide the conditions that are sufficient for the relations $\sigma(A) \subset \Lambda(A)$ or $\Lambda (A) \subset \sigma (A)$ to be satisfied for the band operator $A$.
Access status: Open Access ,
Eigenvalue problems for anisotropic equations involving a potential on Orlicz-Sobolev type spaces
(2016) Stăncuţ, Ionela-Loredana; Stîrcu, Iulia Dorotheea
In this paper we consider an eigenvalue problem that involves a nonhomogeneous elliptic operator, variable growth conditions and a potential $V$ on a bounded domain in $\mathbb{R}^N$ ($N\geq 3$) with a smooth boundary. We establish three main results with various assumptions. The first one asserts that any $\lambda\gt 0$ is an eigenvalue of our problem. The second theorem states the existence of a constant $\lambda_{*}\gt 0$ such that any $\lambda\in(0,\lambda_{*}]$ is an eigenvalue, while the third theorem claims the existence of a constant $\lambda^{*}\gt 0$ such that every $\lambda\in[\lambda^{*}, \infty)$ is an eigenvalue of the problem.
Access status: Open Access ,
Higher order Nevanlinna functions and the inverse three spectra problem
(2016) Boyko, Olga; Martinûk, Ol'ga Mikolaïvna; Pivovarčik, Vâčeslav
The three spectra problem of recovering the Sturm-Liouville equation by the spectrum of the Dirichlet-Dirichlet boundary value problem on $[0,a]$, the Dirichlet-Dirichlet problem on $[0,a/2]$ and the Neumann-Dirichlet problem on $[a/2,a]$ is considered. Sufficient conditions of solvability and of uniqueness of the solution to such a problem are found.
Access status: Restricted ,
Lokalizacja wartości własnych macierzy
(Data obrony: 2011-07-07) Lewińska, Paulina
Wydział Matematyki Stosowanej
Access status: Restricted ,
Macierze Toeplitza i ich zastosowania do dyskretnych modeli procesów stochastycznych
(Data obrony: 2014-07-10) Bęben, Michał
Wydział Matematyki Stosowanej
Access status: Restricted ,
Nierówności dla wybranych wartości własnych pewnych klas macierzy symetrycznych
(Data obrony: 2015-06-26) Kozioł, Wojciech
Wydział Matematyki Stosowanej
Access status: Restricted ,
Odwrotny problem wartości własnych dla macierzy Jacobiego
(Data obrony: 2015-12-17) Kazanecka, Joanna
Wydział Matematyki Stosowanej
Access status: Open Access ,
On Ambarzumian type theorems for tree domains
(Wydawnictwa AGH, 2022) Pivovarčik, Vâčeslav
It is known that the spectrum of the spectral Sturm-Liouville problem on an equilateral tree with (generalized) Neumann's conditions at all vertices uniquely determines the potentials on the edges in the unperturbed case, i.e. case of the zero potentials on the edges (Ambarzumian's theorem). This case is exceptional, and in general case (when the Dirichlet conditions are imposed at some of the pendant vertices) even two spectra of spectral problems do not determine uniquely the potentials on the edges. We consider the spectral Sturm-Liouville problem on an equilateral tree rooted at its pendant vertex with (generalized) Neumann conditions at all vertices except of the root and the Dirichlet condition at the root. In this case Ambarzumian's theorem can't be applied. We show that if the spectrum of this problem is unperturbed, the spectrum of the Neumann-Dirichlet problem on the root edge is also unperturbed and the spectra of the problems on the complimentary subtrees with (generalized) Neumann conditions at all vertices except the subtrees' roots and the Dirichlet condition at the subtrees' roots are unperturbed then the potential on each edge of the tree is 0 almost everywhere.
Access status: Restricted ,
Operatory pseudoodwracalne w sensie Fredholma
(Data obrony: 2016-06-30) Gardian, Rafał
Wydział Matematyki Stosowanej
Access status: Restricted ,
Oszacowania najmniejszych i największych wartości własnych i wartości osobliwych dla pewnych klas macierzy
(Data obrony: 2016-12-21) Śleziak, Agnieszka
Wydział Matematyki Stosowanej
Access status: Open Access ,
Recovering the shape of an equilateral quantum tree with the Dirichlet conditions at the pendant vertices
(Wydawnictwa AGH, 2024) Dudko, Anastasia; Lesechko, Oleksandr; Pivovarchik, Vyacheslav
We consider two spectral problems on an equilateral rooted tree with the standard (continuity and Kirchhoff's type) conditions at the interior vertices (except of the root if it is interior) and Dirichlet conditions at the pendant vertices (except of the root if it is pendant). For the first (Neumann) problem we impose the standard conditions (if the root is an interior vertex) or Neumann condition (if the root is a pendant vertex) at the root, while for the second (Dirichlet) problem we impose the Dirichlet condition at the root. We show that for caterpillar trees the spectra of the Neumann problem and of the Dirichlet problem uniquely determine the shape of the tree. Also, we present an example of co-spectral snowflake graphs
Access status: Restricted ,
Własności spektralne operatorów zwartych
(Data obrony: 2015-07-06) Salwa, Krzysztof
Wydział Matematyki Stosowanej
Access status: Restricted ,
Własności wartości własnych iloczynu macierzy
(Data obrony: 2012-10-22) Piętka, Piotr
Wydział Matematyki Stosowanej
Access status: Restricted ,
Wspólne rozwiązanie równania Lapunowa dla macierzy stowarzyszonej Frobeniusa i macierzy o wymiarach 2x2
(Data obrony: 2013-07-12) Skupień, Sabina
Wydział Matematyki Stosowanej