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1
Content available An inequality for imaginary parts of eigenvalues of non-compact operators with Hilbert-Schmidt Hermitian components
100%
Gil’ M.
Opuscula Mathematica
|
2024
|
tom Vol. 44, no. 2
241--248
EN
Let A be a bounded linear operator in a complex separable Hilbert space, A∗ be its adjoint one and AI := (A − A∗)/(2i). Assuming that AI 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 [formula], where λk(A) (k = 1, 2, . . .) are the eigenvalues of A and N2(·) is the Hilbert-Schmidt norm. In addition, we discuss applications of our results to the Jacobi operators.
2
Content available Korovkin theorem in modular spaces
100%
Bardaro C. , Mantellini I.
Commentationes Mathematicae
|
2007
|
tom 47
|
nr 2
EN
In this paper we obtain an extension of the classical Korovkin theorem in abstract modular spaces. Applications to some discrete and integral operators are discussed.
3
Content available Topological properties of spaces of linear operators on non-locally convex Orlicz spaces
100%
Oelke A.
Commentationes Mathematicae
|
2010
|
tom 50
|
nr 2
EN
We study the topological properties of the space \(\mathcal{L}(L^\varphi, X)\) of all continuous linear operators from an Orlicz space \(L^\varphi\) (an Orlicz function \(\varphi\) is not necessarily convex) to a Banach space \(X\). We provide the space \(\mathcal{L}(L^\varphi ,X)\) with the Banach space structure. Moreover, we examine the space \(\mathcal{L}_s (L^\varphi, X)\) of all singular operators from \(L^\varphi\) to \(X\).
4
Content available remote Approximate controllability of infinite dimensional systems of the n-th order
88%
Respondek J.
International Journal of Applied Mathematics and Computer Science
|
2008
|
tom 18
|
nr 2
199-212
EN
The objective of the article is to obtain general conditions for several types of controllability at once for an abstract differential equation of arbitrary order, instead of conditions for a fixed order equation. This innovative approach was possible owing to analyzing the n-th order linear system in the Frobenius form which generates a Jordan transition matrix of the Vandermonde form. We extensively used the fact that the knowledge of the inverse of a Jordan transition matrix enables us to directly verify the controllability by Chen's theorem. We used the explicit analytical form of the inverse Vandermonde matrix. This enabled us to obtain more general conditions for different types of controllability for infinite dimensional systems than the conditions existing in the literature so far. The methods introduced can be easily adapted to the analysis of other dynamic properties of the systems considered.
5
Content available Best approximation in spaces of bounded linear operators
79%
Lewicki G.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS Chapter 0...............................................................................................................................................................................5    0.1. Introduction..................................................................................................................................................................5    0.2. Preliminary results.......................................................................................................................................................9 Chapter I..............................................................................................................................................................................16    I.1. Best approximation in finite-dimensional subspaces of ℒ(B,D)....................................................................................16    I.2. Kolmogorov's type criteria for spaces of compact operators; general case.................................................................26    I.3. Criteria for the space $K(C_K(T))$.............................................................................................................................30    I.4. The case of sequence spaces....................................................................................................................................38 Chapter II.............................................................................................................................................................................43    II.1. Extensions of linear operators from hyperplanes of $l^{(n)}_∞$.................................................................................43    II.2. Minimal projections onto hyperplanes of $l^{(n)}_1$...................................................................................................52    II.3. Strongly unique minimal projections onto hyperplanes of $l^{(n)}_∞$ and $l^{(n)}_1$...............................................59    II.4. Minimal projections onto subspaces of $l^{(n)}_∞$ of codimension two......................................................................71    II.5. Uniqueness of minimal projections onto subspace of $l^{(n)}_∞$ of codimension two................................................75    II.6. Strong unicity criterion in some space of operators....................................................................................................79 Chapter III.............................................................................................................................................................................83    III.1. Extensions of linear operators from finite-dimensional subspaces I...........................................................................83    III.2. Extensions of linear operators from finite-dimensional subspaces II..........................................................................90    III.3. Algorithms for seeking the constant $W_m$..............................................................................................................97 References..........................................................................................................................................................................99 Index..................................................................................................................................................................................102 Index of symbols................................................................................................................................................................102
6
Content available Simple eigenvectors of unbounded operators of the type "normal plus compact"
75%
Gil M.
Opuscula Mathematica
|
2015
|
tom Vol. 35, no. 2
161--169
EN
The paper deals with operators of the form A = S + B, where B is a compact operator in a Hilbert space H and S is an unbounded normal one in H, having a compact resolvent. We consider approximations of the eigenvectors of A, corresponding to simple eigenvalues by the eigenvectors of the operators An = S + Bn (n = 1, 2,...), where Bn is an n-dimensional operator. In addition, we obtain the error estimate of the approximation.
7
Content available remote On the bivariate Baskakov-Durrmeyer type operators
75%
Krech G. , Malejki R.
Czasopismo Techniczne. Nauki Podstawowe
|
2016
|
tom Y. 113, iss. 1-NP
85--96
EN
In this paper we introduce some linear positive operators of the Baskakov-Durrmeyer type in the space of continuous functions of two variables. The theorems on convergence and the degree of approximation are established.
PL
W artykule definiuje się dodatnie operatory liniowe typu Baskakowa-Durrmeyera w przestrzeni ciągłych funkcji dwóch zmiennych. Formułuje się i dowodzi twierdzenia dotyczące zbieżności oraz rzędu zbieżności.
8
Content available remote About the bivariate operators of Durrmeyer-type
75%
Pop O. , Farcas M.
Demonstratio Mathematica
|
2009
|
tom Vol. 42, nr 1
97-107
EN
The aim of this paper is to study the convergence and approximation properties of the bivariate operators and GBS operators of Durrmeyer-type.
9
A stability property of the generalized shift operator on BMO space
75%
Partyka D.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
1999
|
tom z. 23 [175]
75-84
EN
The supremum norm of the generalized shift operator S phi on the space BMO(R) is estimated, provided phi is an increasing and absolutely continuous homeomorphic self-mapping of R and phi' is an elemnt of BMO(R) andlog phi'II. is small. This result is extended to a locally rectifiable Jordan arc in C which is homeomorphic to R.
10
Content available remote Families of analytic functions associated with the Wright generalized hypergeometric functions
63%
Dziok J. , Raina R. K.
Demonstratio Mathematica
|
2004
|
tom Vol. 37, nr 3
533--542
EN
By introducing a new class of analytic functions with negative coefficients which involves the Wright's generalized hypergeometric function, we investigate the coefficient bounds, distortion theorems, extreme points and radii of convexity and starlikeness for this class of functions.
11
Content available remote A method of microvascular systems analysis based on statistical texture parameter's evaluation
63%
Kulikowski J. L. , Wierzbicka D.
Biocybernetics and Biomedical Engineering
|
2003
|
tom Vol. 23, no. 3
21-37
EN
It is considered a method of computer aided analysis of textures in biomedical images. The method is based on a hierarchy of simple combinatorial tests applied to squareform sub-images on several levels of image analysis. The tests are obtained as a result of combinations of two basic transformations of the original image: restructing and selection. The results of tests are then collected into numerical multi-component vectors and an analysis of vectors similarity is performed. On the basis of evaluated similarity measures a procedure of merging sub-windows covered by similar textures into compact and homogenous segments can be performed. The method is, in particular, oriented to a computer-aided analysis of textures representing micro-vascular systems.
12
Content available remote On linear operators consistent with a subspace in differential spaces
63%
Multarzyński P.
Demonstratio Mathematica
|
2006
|
tom Vol. 39, nr 1
233-244
EN
Linear operators on function and abstract algebras are considered and their consistency with an arbitrary subset or an ideal is studied. Then the consistency concept is formulated for general Poisson brackets in commutative algebras.
13
Content available remote On meromorphic multivalent functions defined with the use of linear operator
63%
Juma A. R. S.
Journal of Mathematics and Applications
|
2011
|
tom Vol. 34
35-44
EN
In the present paper we introduce two classes of meromorphically multivalent functions and application of linear operators on these classes. We study various properties and coefficients bounds, the concept of neighbourhood also investigated.
14
Content available remote Approximate controllability of infinite dimensional systems of the n-th order
63%
Respondek J. S.
International Journal of Applied Mathematics and Computer Science
|
2008
|
tom Vol. 18, no 2
199-212
EN
The objective of the article is to obtain general conditions for several types of controllability at once for an abstract differential equation of arbitrary order, instead of conditions for a fixed order equation. This innovative approach was possible owing to analyzing the n-th order linear system in the Frobenius form which generates a Jordan transition matrix of the Vandermonde form. We extensively used the fact that the knowledge of the inverse of a Jordan transition matrix enables us to directly verify the controllability by Chen’s theorem. We used the explicit analytical form of the inverse Vandermonde matrix. This enabled us to obtain more general conditions for different types of controllability for infinite dimensional systems than the conditions existing in the literature so far. The methods introduced can be easily adapted to the analysis of other dynamic properties of the systems considered.
15
Content available remote Approximation of functions of several variables by the Baskakov-Durrmeyer type operators
63%
Krech I. , Malejki R.
Czasopismo Techniczne. Nauki Podstawowe
|
2016
|
tom Y. 113, iss. 1-NP
97--105
EN
In this paper we introduce some linear positive operators of the Baskakov-Durrmeyer type in the space of uniformly continuous and bounded functions of several variables. The theorem on the degree of the convergence is established. Moreover, we give the Voronovskaya type formula for these operators.
PL
W artykule rozważa się operatory typu Baskakowa-Durrmeyera w przestrzeni ograniczonych i jednostajnie ciągłych funkcji wielu zmiennych. Formułuje się i dowodzi twierdzenia dotyczące rzędu zbieżności, jak również twierdzenie typu Woronowskiej dla tych operatorów.
16
Content available remote Optimal supervisory control of regular languages
63%
Ray A. , Fu J. , Lagoa C.
Demonstratio Mathematica
|
2004
|
tom Vol. 37, nr 4
991--1013
EN
This paper presents an algorithm for optimal control of regular languages, realized as deterministic finite state automata (DFSA), with (possible) penalty on event disabling. A signed real measure quantifies the behavior of controlled sublanguages based on a state transition cost matrix and a characteristic vector as reported in an earlier publication. The performance index for the proposed optimal policy is obtained by combining the measure of the supervised plant language with the cost of disabled controllable event(s). Synthesis of this optimal control policy requires at most n iterations, where n is the number of states of the DFSA model generated from the unsupervised regular language. The computational complexity of the optimal control synthesis is polynomial in n. The control algorithms are illustrated with an application example of a twin-engine surveillance aircraft.
17
Content available remote On some right invertible operators in differential spaces
63%
Multarzyński P.
Demonstratio Mathematica
|
2004
|
tom Vol. 37, nr 4
905--920
EN
In this paper we consider the right invertibility problem of some linear operators defined on the algebra of smooth function on a differential space.
18
Classes of functions related to the generalized hypergeometric function
51%
Leś-Bomba E.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
2004
|
tom z. 27 [212]
29-37
EN
In this paper we Investigate a class of p-valent analytic functions with fixed argument of coefficient, which is defined in terms of generalized hypergeometric function. Using techniques due to Dziok and Srivastava [4] (see also [1]) we investigate coefficient estimates, distortion theorems, the radii of convexity and starlikeness in this class.
19
Content available remote Order properties of the space of A-linear operators
51%
Turan B.
Demonstratio Mathematica
|
2006
|
tom Vol. 39, nr 2
429-438
EN
Let A be an f-algebra with unit and L, M be two topologically full f-modules on A. We prove that the space of A-linear operators Lb(L, M; A) is a Riesz space and we study the order properties of the adjoint operator from Lb(L, M; A) to Lb(M~, L~; (A)^n). The main result given here describes the centre of the space of Lb{L, M; A).
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