Browsing by Subject "eigenvalues"

Now showing 1 - 13 of 13

Access status: Open Access ,
An inequality for imaginary parts of eigenvalues of non-compact operators with Hilbert-Schmidt Hermitian components
(Wydawnictwa AGH, 2024) Gil', Michael
Let $A$ be a bounded linear operator in a complex separable Hilbert space, $A^{*}$ be its adjoint one and $A_I:=(A-A^*)/(2i)$. Assuming that $A_I$ is a Hilbert-Schmidt operator, we investigate perturbations of the imaginary parts of the eigenvalues of $A$. Our results are formulated in terms of the »extended« eigenvalue sets in the sense introduced by T. Kato. Besides, we refine the classical Weyl inequality $\sum_{k=1}^\infty (\operatorname{Im} \lambda_k(A))^2 \leq N_2^2(A_I)$, where $\lambda_{k}(A)$ $(k=1,2, \ldots )$ are the eigenvalues of $A$ and $N_2(\cdot)$ is the Hilbert-Schmidt norm. In addition, we discuss applications of our results to the Jacobi operators.
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 ,
Hyponormal differential operators with discrete spectrum
(2010) Ismailov, Zameddin I.; Unluyol, Erdal
In this work, we first describe all the maximal hyponormal extensions of a minimal operator generated by a linear differential-operator expression of the first-order in the Hilbert space of vector-functions in a finite interval. Next, we investigate the discreteness of the spectrum and the asymptotical behavior of the modules of the eigenvalues for these maximal hyponormal extensions.
Access status: Open Access ,
Linear Sturm-Liouville problems with Riemann-Stieltjes integral boundary conditions
(Wydawnictwa AGH, 2018) Kong, Qingkai; George, Thomas E. St.
We study second-order linear Sturm-Liouville problems involving general homogeneous linear Riemann-Stieltjes integral boundary conditions. Conditions are obtained for the existence of a sequence of positive eigenvalues with consecutive zero counts of the eigenfunctions. Additionally, we find interlacing relationships between the eigenvalues of such Sturm-Liouville problems and those of Sturm-Liouville problems with certain two-point separated boundary conditions.
Access status: Restricted ,
Lokalizacja wartości własnych macierzy i operatorów
(Data obrony: 2016-11-17) Rusek, Joanna
Wydział Matematyki Stosowanej
Access status: Restricted ,
Macierze normalne
(Data obrony: 2013-07-12) Kamiński, Adrian
Wydział Matematyki Stosowanej
Access status: Open Access ,
On small vibrations of a damped Stieltjes string
(2015) Boyko, Olga; Pivovarchik, Vyacheslav
Inverse problem of recovering masses, coefficients of damping and lengths of the intervals between the masses using two spectra of boundary value problems and the total length of the Stieltjes string (an elastic thread bearing point masses) is considered. For the case of point-wise damping at the first counting from the right end mass the problem of recovering the masses, the damping coefficient and the lengths of the subintervals by one spectrum and the total length of the string is solved.
Access status: Open Access ,
On spectra of quadratic operator pencils with rank one gyroscopic linear part
(Wydawnictwa AGH, 2018) Bojko, Olga Pavlìvna; Martinûk, Olʹga Mikolaïvna; Pivovarčik, Vâčeslav
The spectrum of a selfadjoint quadratic operator pencil of the form $\lambda^2M-\lambda G-A$ is investigated where $M\geq 0$, $G\geq 0$ are bounded operators and $A$ is selfadjoint bounded below is investigated. It is shown that in the case of rank one operator $G$ the eigenvalues of such a pencil are of two types. The eigenvalues of one of these types are independent of the operator $G$. Location of the eigenvalues of both types is described. Examples for the case of the Sturm-Liouville operators $A$ are given.
Access status: Restricted ,
Podobieństwo macierzy w przestrzeniach z nieoznaczonym iloczynem skalarnym
(Data obrony: 2018-02-14) Wróbel, Mariusz
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 ,
Stochastic differential equations for random matrices processes in the nonlinear framework
(Wydawnictwa AGH, 2018) Stihi, Sara; Boutabia, Hacène; Meradji, Selma
In this paper, we investigate the processes of eigenvalues and eigenvectors of a symmetric matrix valued process $X_{t}$, where $X_{t}$ is the solution of a general SDE driven by a $G$-Brownian motion matrix. Stochastic differential equations of these processes are given. This extends results obtained by P. Graczyk and J. Malecki in [Multidimensional Yamada-Watanabe theorem and its applications to particle systems, J. Math. Phys. 54 (2013), 021503].
Access status: Open Access ,
The approximate location of imperfection in a unit circle using the spectrum of Laplace operator as a research tool
(Wydawnictwa AGH, 2015) Brzęk, Mateusz; Zagórowska, Marta; Mitkowski, Wojciech
W artykule przeanalizowano zastosowanie widma operatora Laplace'a jako narzędzia do przybliżonej lokalizacji uszkodzeń w kole jednostkowym. W części teoretycznej zdefiniowano zagadnienie spektralne rozwiązywane za pomocą wartości własnych. Znalezione wartości zależą od położenia i rozmiaru uszkodzeń. W artykule został zdefiniowany problem odwrotny, który polega na znalezieniu miejsca uszkodzenia na podstawie znanego widma.
Access status: Open Access ,
Variational characterizations for eigenfunctions of analytic self-adjoint operator functions
(2013) Katsouleas, Georgios; Maroulas, John
In this paper we consider Rellich’s diagonalization theorem for analytic self-adjoint operator functions and investigate variational principles for their eigenfunctions and interlacing statements. As an application, we present a characterization for the eigenvalues of hyperbolic operator polynomials.