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1
Content available An inequality for imaginary parts of eigenvalues of non-compact operators with Hilbert-Schmidt Hermitian components
Gil’ Michael
Opuscula Mathematica
|
2024
|
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 remote On the bivariate Baskakov-Durrmeyer type operators
Krech G., Malejki R.
Czasopismo Techniczne. Nauki Podstawowe
|
2016
|
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.
3
Content available remote Approximation of functions of several variables by the Baskakov-Durrmeyer type operators
Krech I., Malejki R.
Czasopismo Techniczne. Nauki Podstawowe
|
2016
|
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.
4
Content available Simple eigenvectors of unbounded operators of the type "normal plus compact"
Gil M.
Opuscula Mathematica
|
2015
|
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.
5
Content available remote On meromorphic multivalent functions defined with the use of linear operator
Juma A. R. S.
Journal of Mathematics and Applications
|
2011
|
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.
6
Content available remote About the bivariate operators of Durrmeyer-type
Pop O., Farcas M.
Demonstratio Mathematica
|
2009
|
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.
7
Content available remote Approximate controllability of infinite dimensional systems of the n-th order
Respondek J. S.
International Journal of Applied Mathematics and Computer Science
|
2008
|
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.
8
Content available remote Order properties of the space of A-linear operators
Turan B.
Demonstratio Mathematica
|
2006
|
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).
9
Content available remote On linear operators consistent with a subspace in differential spaces
Multarzyński P.
Demonstratio Mathematica
|
2006
|
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.
10
Classes of functions related to the generalized hypergeometric function
Leś-Bomba Edyta
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
2004
|
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.
11
Content available remote Optimal supervisory control of regular languages
Ray A., Fu J., Lagoa C.
Demonstratio Mathematica
|
2004
|
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.
12
Content available remote On some right invertible operators in differential spaces
Multarzyński P.
Demonstratio Mathematica
|
2004
|
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.
13
Content available remote Families of analytic functions associated with the Wright generalized hypergeometric functions
Dziok J., Raina R. K.
Demonstratio Mathematica
|
2004
|
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.
14
Content available remote Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex space
Shkarin S. S.
Demonstratio Mathematica
|
2003
|
Vol. 36, nr 3
611--626
EN
According to Mickael's selection theorem any surjective continuous linear operator from one Prechet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if E is a Frechet space and T : E -> E is a continuous linear operator such that the Cauchy problem x = T x, x(0) = X0 is solvable in [0,1] for any X06 E, then for anyf zawiera się C([0, 1],E), there exists a continues map S : [0,1] x E -> E, (t x) ->o StX such that for any X0 zawiera się w E, the function x(t) = StX0 is a solution of the Cauchy problem x(t) = Tx(t) +- f(t), x(0) = X0 (they call S a fundamental system of solutions of the equation x = Tx + f). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Frechet spaces and strong duals of Frechet-Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.
15
Content available remote A method of microvascular systems analysis based on statistical texture parameter's evaluation
Kulikowski J. L., Wierzbicka D.
Biocybernetics and Biomedical Engineering
|
2003
|
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.
16
On the subclassesof functions connected with some linear operators
Patel J., Sahoo P., Stankiewicz J.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
2001
|
z. 25 [190]
151-165
EN
The object of the present paper is to introduce two subclasses Bk,p (a, c) and Ck,p (a, c) of analytic functions in the open unit disc involving a linear operator [...] (a, c) and derive some properties of these classes.
17
A stability property of the generalized shift operator on BMO space
Partyka D.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
1999
|
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.
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