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Tytuł:
Matrix polynomials orthogonal with respect to a non-symmetric matrix of measures
Autorzy:
Zygmunt, M. J.
Powiązania:
https://bibliotekanauki.pl/articles/255142.pdf
Data publikacji:
2016
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
matrix orthogonal polynomials
recurrence formula
matrix of measures
block Jacobi matrices
Opis:
The paper focuses on matrix-valued polynomials satisfying a three-term recurrence relation with constant matrix coefficients. It is shown that they form an orthogonal system with respect to a matrix of measures, not necessarily symmetric. Moreover, it is stated the condition on the coefficients of the recurrence formula for which the matrix measure is symmetric.
Źródło:
Opuscula Mathematica; 2016, 36, 3; 409-423
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Asymptotic behaviour and approximation of eigenvalues for unbounded block Jacobi matrices
Autorzy:
Malejki, M.
Powiązania:
https://bibliotekanauki.pl/articles/255505.pdf
Data publikacji:
2010
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
symmetric unbounded Jacobi matrix
block Jacobi matrix
tridiagonal matrix
point spectrum
eigenvalue
asymptotics
Opis:
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 x pn, where N = max{k ∈ N : k ≤ rpn} and r ∈ (0, 1) is suitably chosen. We apply this result to obtain the asymptotics of the eigenvalues of J in the case p = 3.
Źródło:
Opuscula Mathematica; 2010, 30, 3; 311-330
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the $S$-matrix of Schrödinger operator with nonlocal $\delta$-interaction
Autorzy:
Główczyk, Anna
Kużel, Sergiusz
Powiązania:
https://bibliotekanauki.pl/articles/2051910.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Lax-Phillips scattering scheme
scattering matrix
S-matrix
nonlocal -interaction
non-cyclic function
Opis:
Schrodinger operators with nonlocal δ-interaction are studied with the use of the Lax-Phillips scattering theory methods. The condition of applicability of the Lax-Phillips approach in terms of non-cyclic functions is established. Two formulas for the S-matrix are obtained. The first one deals with the Krein-Naimark resolvent formula and the Weyl-Titchmarsh function, whereas the second one is based on modified reflection and transmission coefficients. The S-matrix S(z) is analytical in the lower half-plane $\mathbb{C}$_ when the Schrodinger operator with nonlocal δ-interaction is positive self-adjoint. Otherwise, S(z) is a meromorphic matrix-valued function in $\mathbb{C}$_ and its properties are closely related to the properties of the corresponding Schrodinger operator. Examples of S-matrices are given.
Źródło:
Opuscula Mathematica; 2021, 41, 3; 413-435
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new method for solving ill-conditioned linear systems
Autorzy:
Soleymani, F.
Powiązania:
https://bibliotekanauki.pl/articles/256033.pdf
Data publikacji:
2013
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
matrix inversion
linear systems
Hilbert matrix
ill-conditioned
approximate inverse
Opis:
An accurate numerical method is established for matrix inversion. It is shown theoretically that the scheme possesses the high order of convergence of seven. Subsequently, the method is taken into account for solving linear systems of equations. The accuracy of the contributed iterative method is clarified on solving numerical examples when the coefficient matrices are ill-conditioned. All of the computations are performed on a PC using several programs written in MATHEMATICA 7.
Źródło:
Opuscula Mathematica; 2013, 33, 2; 337-344
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solution of the Stieltjes truncated matrix moment problem
Autorzy:
Adamyan, V.M.
Tkachenko, I.M.
Powiązania:
https://bibliotekanauki.pl/articles/255081.pdf
Data publikacji:
2005
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Stieltjes power moments
canonical solutions
Nevanlinna's formula
matrix
Opis:
The truncated Stieltjes matrix moment problem consisting in the description of all matrix distributions sigma(t) on [0, infin) with given first 2n + 1 power moments (Cj)nj=0 is solved using known results on the corresponding Hamburger problem for which sigma(t) are defined on (-infin, infin). The criterion of solvability of the Stieltjes problem is given and all its solutions in the non-degenerate case are described by selection of the appropriate solutions among those of the Hamburger problem for the same set of moments. The results on extensions of non-negative operators are used and a purely algebraic algorithm for the solution of both Hamburger and Stieltjes problems is proposed.
Źródło:
Opuscula Mathematica; 2005, 25, 1; 5-24
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Asymptotics of the discrete spectrum for complex Jacobi matrices
Autorzy:
Malejki, M.
Powiązania:
https://bibliotekanauki.pl/articles/255272.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
tridiagonal matrix
complex Jacobi matrix
discrete spectrum
eigenvalue
asymptotic formula
unbounded operator
Riesz projection
Opis:
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 l2(N).
Źródło:
Opuscula Mathematica; 2014, 34, 1; 139-160
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Non symmetric random walk on infinite graph
Autorzy:
Zygmunt, M. J.
Powiązania:
https://bibliotekanauki.pl/articles/254997.pdf
Data publikacji:
2011
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
random walk on an infinite graph
block tridiagonal transition matrix
spectral measure matrix orthogonal polynomials
Opis:
We investigate properties of a non symmetric Markov's chain on an infinite graph. We show the connection with matrix valued random walk polynomials which satisfy the orthogonality formula with respect to non a symmetric matrix valued measure.
Źródło:
Opuscula Mathematica; 2011, 31, 4; 669-674
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Discrete spectra for some complex infinite band matrices
Autorzy:
Malejki, Maria
Powiązania:
https://bibliotekanauki.pl/articles/2048983.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
unbounded operator
band-type matrix
complex tridiagonal matrix
discrete spectrum
eigenvalue
limit points of eigenvalues
Opis:
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 $\Lambda(A)=\{\lambda \in Lim_{n \rightarrow \infty} \lambda_{n}: \lambda_{n}$ is an eigenvalue of $A_{n}$ for $n \geq 1\}$ where $Lim_{n \rightarrow \infty} \lambda_{n}$ is the set of all limit points of the sequence (λn) and An is a finite dimensional orthogonal truncation of A. The aim of this article is to provide the conditions that are sufficient for the relations σ (A) ⊂ Λ (A) or Λ(A) ) ⊂ σ (A) to be satisfied for the band operator A.
Źródło:
Opuscula Mathematica; 2021, 41, 6; 861-879
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Limit-point criteria for the matrix Sturm-Liouville operator and its powers
Autorzy:
Braeutigam, I. N.
Powiązania:
https://bibliotekanauki.pl/articles/255833.pdf
Data publikacji:
2017
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
quasi-derivative
quasi-differential operator
matrix Sturm-Liouville operator
deficiency numbers
distributions
Opis:
We consider matrix Sturm-Liouville operators generated by the formal expression [formula] in the space [formula]. Let the matrix functions P := P(x), Q := Q(x) and R := R(x) of order n (n ∈ N) be defined on I, P is a nondegenerate matrix, P and Q are Hermitian matrices for x ∈ I and the entries of the matrix functions[formula], Q and R are measurable on I and integrable on each of its closed finite subintervals. The main purpose of this paper is to find conditions on the matrices P, Q and R that ensure the realization of the limit-point case for the minimal closed symmetric operator generated by [formula]. In particular, we obtain limit-point conditions for Sturm-Liouville operators with matrix-valued distributional coefficients.
Źródło:
Opuscula Mathematica; 2017, 37, 1; 5-19
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximation of eigenvalues of some unbounded self-adjoint discrete Jacobi matrices by eigenvaules of finite submatrices
Autorzy:
Malejki, M.
Powiązania:
https://bibliotekanauki.pl/articles/255561.pdf
Data publikacji:
2007
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
self-adjoint unbounded Jacobi matrix
asymptotics
point spectrum
tridiagonal matrix
eigenvalue
Opis:
We investigate the problem of approximation of eigenvalues of some self-adjoint operator in the Hilbert space l2(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 → ∞) 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 x n. The method applied in our research is based on the Rayleigh-Ritz method and Volkmer's results included in [7]. We extend the method to cover a class of infinite symmetric Jacobi matrices with three diagonals satisfying some polynomial growth estimates.
Źródło:
Opuscula Mathematica; 2007, 27, 1; 37-49
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Asymptotic expansion of large eigenvalues for a class of unbounded Jacobi matrices
Autorzy:
Harrat, Ayoub
Zerouali, El Hassan
Zielinski, Lech
Powiązania:
https://bibliotekanauki.pl/articles/255073.pdf
Data publikacji:
2020
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
tridiagonal matrix
band matrix
unbounded self-adjoint operator discrete spectrum
large eigenvalues
asymptotics
Opis:
We investigate a class of infinite tridiagonal matrices which define unbounded self-adjoint operators with discrete spectrum. Our purpose is to establish the asymptotic expansion of large eigenvalues and to compute two correction terms explicitly.
Źródło:
Opuscula Mathematica; 2020, 40, 2; 241-270
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the eigenvalues of a 2 x 2 block operator matrix
Autorzy:
Muminov, M. I.
Rasulov, T. H.
Powiązania:
https://bibliotekanauki.pl/articles/254735.pdf
Data publikacji:
2015
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
block operator matrix
Fock space
discrete and essential spectra
Birman-Schwinger principle
Efimov effect
discrete spectrum asymptotics
embedded eigenvalues
Opis:
A 2 x 2 block operator matrix H acting in the direct sum of one- and two-particle subspaces of a Fock space is considered. The existence of infinitely many negative eigenvalues of H22 (the second diagonal entry of H) is proved for the case where both of the associated Friedrichs models have a zero energy resonance. For the number N(z) of eigenvalues of H22 lying below z < 0, the following asymptotics is found [formula]. Under some natural conditions the infiniteness of the number of eigenvalues located respectively inside, in the gap, and below the bottom of the essential spectrum of H is proved.
Źródło:
Opuscula Mathematica; 2015, 35, 3; 371-395
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Circulant matrices: norm, powers, and positivity
Autorzy:
Lindner, M.
Powiązania:
https://bibliotekanauki.pl/articles/255337.pdf
Data publikacji:
2018
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
spectral norm
circulant matrix
eventually positive semigroups
Opis:
In their recent paper "The spectral norm of a Horadam circulant matrix", Merikoski, Haukkanen, Mattila and Tossavainen study under which conditions the spectral norm of a general real circulant matrix C equals the modulus of its row/column sum. We improve on their sufficient condition until we have a necessary one. Our results connect the above problem to positivity of sufficiently high powers of the matrix CTC. We then generalize the result to complex circulant matrices.
Źródło:
Opuscula Mathematica; 2018, 38, 6; 849-857
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Maximum packings of the a-fold complete 3-uniform hypergraph with loose 3-cycles
Autorzy:
Bunge, Ryan C.
Collins, Dontez
Conko-Camel, Daryl
El-Zanati, Saad I.
Liebrecht, Rachel
Vasquez, Alexander
Powiązania:
https://bibliotekanauki.pl/articles/255534.pdf
Data publikacji:
2020
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
tridiagonal matrix
band matrix
unbounded self-adjoint operator discrete spectrum
large eigenvalues
asymptotics
Opis:
It is known that the 3-uniform loose 3-cycle decomposes the complete 3-uniform hypergraph of order v if and only if v ≡0, 1, or 2 (mod 9). For all positive integers λand v, we find a maximum packing with loose 3-cycles of the λ-fold complete 3-uniform hypergraph of order v. We show that, if v ≥6, such a packing has a leave of two or fewer edges.
Źródło:
Opuscula Mathematica; 2020, 40, 2; 209-225
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Compactly supported multi-wavelets
Autorzy:
Banaś, W.
Powiązania:
https://bibliotekanauki.pl/articles/255374.pdf
Data publikacji:
2012
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
compactly supported multi-wavelet
compactly supported scaling function
multiresolution analysis
expansive matrix
Opis:
In this paper we show some construction of compactly supported multi-wavelets In L2(Rd), d ≥ 2 which is based on the one-dimensional case, when d = 1. We also demonstrate that some methods, which are useful in the construction of wavelets with a compact support at d = 1, can be adapted to higher-dimensional cases if A ∈Mdxd(Z) is an expansive matrix of a special form.
Źródło:
Opuscula Mathematica; 2012, 32, 1; 21-29
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 50

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