Browsing by Subject "spectrum"

Now showing 1 - 20 of 21

Access status: Open Access ,
A note on Hausdorff convergence of pseudospectra
(Wydawnictwa AGH, 2023) Lindner, Marko; Schmeckpeper, Dennis
For a bounded linear operator on a Banach space, we study approximation of the spectrum and pseudospectra in the Hausdorff distance. We give sufficient and necessary conditions in terms of pointwise convergence of appropriate spectral quantities.
Access status: Open Access ,
Analiza spektralna stóp zwrotu dla spółek z indeksu SMI
(2010) Gurgul, Henryk; Kłęk, Krzysztof
Celem artykułu jest zastosowanie analizy spektralnej do zbadania struktury i częstotliwości szeregów czasowych stóp zwrotu 19 spółek notowanych w indeksie SMI, będącym głównym indeksem giełdy szwajcarskiej. Zbadano też za pomocą metod spektralnych, czy istnieje zależność pomiędzy stopami zwrotu wybranych pięciu spółek reprezentujących pięć głównych branż gospodarki szwajcarskiej. Uzyskane wyniki świadczą o braku istnienia takiej zależności. Nie stwierdzono w szczególności istotnej zależności pomiędzy składowymi częstotliwościami par szeregów czasowych.
Access status: Open Access ,
Application of Green's operator to quadratic variational problems
(2006) Azbelev, Nikolay V.; Tsalyuk, Vadim Z.
We use Green’s function of a suitable boundary value problem to convert the variational problem with quadratic functional and linear constraints to the equivalent unconstrained extremal problem in some subspace of the space $L_{2}$ of quadratically summable functions. We get the neccessary and sufficient criterion for unique solvability of the variational problem in terms of the spectrum of some integral Hilbert–Schmidt operator in $L_{2}$ with symmetric kernel. The numerical technique is proposed to estimate this criterion. The results are demonstrated on examples: 1) a variational problem with deviating argument, and 2) the problem of the critical force for the vertical pillar with additional support point (the qualities of the pillar may vary discontinuously along the pillar’s axis).
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 ,
Asymptotyczny rozkład wartości własnych dla pewnych macierzy typu Jacobiego
(Data obrony: 2014-07-10) Banach, Agnieszka
Wydział Matematyki Stosowanej
Access status: Restricted ,
Asymptotyka spektralna ciągów macierzy trójdiagonalnych
(Data obrony: 2012-10-19) Sandomierska, Joanna
Wydział Matematyki Stosowanej
Access status: Open Access ,
Eigenvalue-eigenfunction problem for Steklov's smoothing operator and differential-difference equations of mixed type
(2013) Âkovlev, Sergej I.; Âkovleva, Valentina
It is shown that any $\mu \in \mathbb{C}$ is an infinite multiplicity eigenvalue of the Steklov smoothing operator $S_h$ acting on the space $L^1_{loc}(\mathbb{R})$. For $\mu \neq 0$ the eigenvalue-eigenfunction problem leads to studying a differential-difference equation of mixed type. An existence and uniqueness theorem is proved for this equation. Further a transformation group is defined on a countably normed space of initial functions and the spectrum of the generator of this group is studied. Some possible generalizations are pointed out.
Access status: Open Access ,
Ergodic conditions and spectral properties for A-contractions
(2008) Suciu, Laurian; Suciu, Nicolae
In this paper the canonical representation of an $A$-contraction $T$ on a Hilbert space $\mathcal{H}$ is used to obtain some conditions concerning the concept of $A$-ergodicity studied in [L. Suciu, <i>Orthogonal decompositions induced by generalized contractions</i>, Acta Sci. Math. (Szeged) 70 (2004), 751–765; L. Suciu, On the ergodic $A$-contractions, Analele Universitaţii de Vest din Timişoara, Ser. Mat.-Inf. 2 (2004), 115–136; L. Suciu, Ergodic properties for regular $A$-contractions, Integral Equations and Operator Theory 56 (2006) 2, 285–299; L. Suciu, <i>Ergodic properties and saturation for A-contractions, Operator Theory: Advances and Applications</i>; Proceeding of 20th Conference on Operator Theory, Timişoara 2004, Theta 2006, 225–242]. The regular case and the case of $\mathcal{R}(A)$ closed are considered, and specifically, the $TT^{*}$-contractions are studied. Some spectral properties are also given for certain particular class of $A$-isometries.
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: Open Access ,
Matrices defined by frames
(2009) Ambroziński, Zbigniew; Rudol, Krzysztof
Matrix representations of bounded Hilbert space operators are considered. The matrices in question are defined with respect to frames, rather than bases. The frames, a generalisation of bases, used extensively in applied harmonic analysis, are overcomplete sequences. We consider some properties related to tight frames, where, up to some multiplicative constant, a form of Parseval Identity takes place. We also describe parts of spectra of operators in terms of their matrices.
Access status: Restricted ,
Metoda iteracyjno-projekcyjna dla pewnej klasy równań różnicowych
(Data obrony: 2013-07-23) Gorzkowska, Aleksandra
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 the extended and Allan spectra and topological radii
(2012) Arizmendi, Hugo; Carrillo-Hoyo, Angel Manuel; Roa-Fajardo, Jairo
In this paper we prove that the extended spectrum $\Sigma(x)$, defined by W. Żelazko, of an element $x$ of a pseudo-complete locally convex unital complex algebra $A$ is a subset of the spectrum $\sigma_A(x)$, defined by G.R. Allan. Furthermore, we prove that they coincide when $\Sigma(x)$ is closed. We also establish some order relations between several topological radii of $x$, among which are the topological spectral radius $R_t(x)$ and the topological radius of boundedness $\beta_t(x)$.
Access status: Metadata only ,
Operatory typu Fredholma i ich zastosowanie w teorii transportu
(Data obrony: 2012-07-10) Kras, Monika
Wydział Matematyki Stosowanej
Access status: Restricted ,
Proste i odwrotne problemy spektralne dla macierzy typu Jacobiego
(Data obrony: 2015-12-17) Łysakowski, Jarosław
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 ,
Różne dowody twierdzenia spektralnego
(Data obrony: 2012-09-19) Gruszecki, Bartosz
Wydział Matematyki Stosowanej
Access status: Open Access ,
Spectrum localization of a perturbed operator in a strip and applications
(Wydawnictwa AGH, 2021) Gil', Michael
Let $A$ and $\tilde{A}$ be bounded operators in a Hilbert space. We consider the following problem: let the spectrum of $A$ lie in some strip. In what strip the spectrum of $\tilde{A}$ lies if $A$ and $\tilde{A}$ are »close«? Applications of the obtained results to integral operators and matrices are also discussed. In addition, we apply our perturbation results to approximate the spectral strip of a Hilbert-Schmidt operator by the spectral strips of finite matrices.
Access status: Open Access ,
Spectrum of J-frame operators
(Wydawnictwa AGH, 2018) Giribet, Juan Ignacio; Langer, Matthias; Leben, Leslie; Maestripieri, Alejandra; Martínez Pería, Francisco; Trunk, Carsten
A $J$-frame is a frame $\mathcal{F}$ for a Krein space $(\mathcal{H},[\cdot,\cdot ])$ which is compatible with the indefinite inner product $[\cdot,\cdot ]$ in the sense that it induces an indefinite reconstruction formula that resembles those produced by orthonormal bases in $\mathcal{H}$. With every $J$-frame the so-called $J$-frame operator is associated, which is a self-adjoint operator in the Krein space $\mathcal{H}$. The $J$-frame operator plays an essential role in the indefinite reconstruction formula. In this paper we characterize the class of $J$-frame operators in a Krein space by a $2\times 2$ block operator representation. The $J$-frame bounds of $\mathcal{F}$ are then recovered as the suprema and infima of the numerical ranges of some uniformly positive operators which are build from the entries of the $2\times 2$ block representation. Moreover, this $2\times 2$ block representation is utilized to obtain enclosures for the spectrum of $J$-frame operators, which finally leads to the construction of a square root. This square root allows a complete description of all $J$-frames associated with a given $J$-frame operator.
Access status: Restricted ,
Stabilność wypukłych zbiorów macierzy
(Data obrony: 2015-07-13) Lacher, Katarzyna
Wydział Matematyki Stosowanej