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1
Content available remote A reconstruction method of generalized sampling based on generalized inverse
100%
Zhaoxuan Z. , Houjun W. , Zhigang W. , Hao Z.
|
2010
|
tom Vol. 17, nr 2
163-171
EN
This paper considers the problem of reconstructing a class of generalized sampled signals of which a special case occurs in, e.g., a generalized sampling system due to non-ideal analysis basis functions. To this end, we propose an improved reconstruction system and a reconstruction algorithm based on generalized inverse, which can be viewed as a reconstruction method that reduces reconstruction error as well. The key idea is to add an additional channel into a generalized sampling system and apply the generalized inverse theory to the reconstruction algorithm. Finally, the approach is applied, respectively, to an oscilloscope, which shows the proposed method yields better performance as compared to the existing technique.
2
Content available remote Broadband microwave correlator of noise signals
100%
Susek W. , Stec B.
|
2010
|
tom Vol. 17, nr 2
289-297
EN
A real narrowband noise signal representation in the form of an analytical signal in the Hilbert space is presented in the paper. This analytical signal is illustrated in a variable complex plane as a mark with defined amplitude, phase, pulsation and instantaneous frequency. A block diagram of a broadband product detector in a quadrature system is presented. Measurement results of an autocorrelation function of a noise signal are shown and the application of such solution in a noise radar for precise determination of distance changes as well as velocities of these changes are also presented. Conclusions and future plans for applications of the presented detection technique in broadband noise radars bring the paper to an end.
3
Content available remote Unbounded Hermitian operators and relative reproducing kernel Hilbert space
100%
Jorgensen P.
Open Mathematics
|
2010
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tom 8
|
nr 3
569-596
EN
We study unbounded Hermitian operators with dense domain in Hilbert space. As is known, the obstruction for a Hermitian operator to be selfadjoint or to have selfadjoint extensions is measured by a pair of deficiency indices, and associated deficiency spaces; but in practical problems, the direct computation of these indices can be difficult. Instead, in this paper we identify additional structures that throw light on the problem. We will attack the problem of computing deficiency spaces for a single Hermitian operator with dense domain in a Hilbert space which occurs in a duality relation with a second Hermitian operator, often in the same Hilbert space.
4
Pole assignment of the coupled generalized system.
100%
Zhaoqiang G. , Yonghao M.
|
2000
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tom Vol. 26, nr 3
5-14
EN
In mathematical and engineering control theory it is of great importance that the control system is described by the coupled generalized control system. One of the most important problems is to study the stabilization and pole assignment. In the paper, the pole assignment of the coupled generalized control system is discussed in Hilbert space. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse of one operator.
5
Content available remote A Simple Proof of the Polar Decomposition Theorem
100%
Wójcik P.
Annales Mathematicae Silesianae
|
2017
|
tom 31
|
nr 1
165-171
EN
In this expository paper, we present a new and easier proof of the Polar Decomposition Theorem. Unlike in classical proofs, we do not use the square root of a positive matrix. The presented proof is accessible to a broad audience.
6
Content available remote Gradient method for non-injective operators in Hilbert space with application to Neumann problems
100%
Karátson J.
Applicationes Mathematicae
|
1999
|
tom 26
|
nr 3
333-346
EN
The gradient method is developed for non-injective non-linear operators in Hilbert space that satisfy a translation invariance condition. The focus is on a class of non-differentiable operators. Linear convergence in norm is obtained. The method can be applied to quasilinear elliptic boundary value problems with Neumann boundary conditions.
7
Content available remote A new view of some operators and their properties in terms of the Non-Newtonian Calculus
100%
Ünlüyol E. , Salas S. , Iscan I.
Topological Algebra and its Applications
|
2017
|
tom 5
|
nr 1
49-54
EN
Differentiation and integration are basic operations of calculus and analysis. Indeed, they are in- finitesimal versions of substraction and addition operations on numbers, respectively. From 1967 till 1970 Michael Grossman and Robert Katz gave definitions of a new kind of derivative and integral, converting the roles of substraction and addition into division and multiplication, respectively and thus established a new calculus, called Non-Newtonian Calculus. So in this paper, it is investigated to a new view of some operators and their properties in terms of Non-Newtonian Calculus. Then we compare with the Newtonian and Non-Newtonian Calculus.
8
Content available remote Operator fractional-linear transformations: convexity and compactness of image; applications
100%
Khatskevich V. , V. Shul'Man
Studia Mathematica
|
1995
|
tom 116
|
nr 2
189-195
EN
The present paper consists of two parts. In Section 1 we consider fractional-linear transformations (f.-l.t. for brevity) F in the space $ℒ(X_1,X_2)$ of all linear bounded operators acting from $X_1$ into $X_2$, where $X_1, X_2$ are Banach spaces. We show that in the case of Hilbert spaces $X_1, X_2$ the image F(ℬ) of any (open or closed) ball ℬ ⊂ D(F) is convex, and if ℬ is closed, then F(ℬ) is compact in the weak operator topology (w.o.t.) (Theorem 1.2). These results extend the corresponding results on compactness obtained in [3], [4] under some additional restrictions imposed on F. We also establish that the convexity of the image of f.-l.t. is a characteristic property of Hilbert spaces, that is, if for the f.-l.t. $F:K → (I+K)^{-1}$ the image $F(𝘒)$ of the open unit ball 𝘒 of the space ℒ(X) is convex, then X is a Hilbert space (Theorem 1.3). In Section 2 we apply the compactness of F(𝘒̅) for the closed unit operator ball 𝘒̅ to the study of the behavior of solutions to evolution problems in a Hilbert space ℋ. Namely, we establish the exponential dichotomy of solutions for the so-called hyperbolic case (such that the evolution operator is invertible). This is an extension of Theorem 1.1 of [5], where the corresponding assertion was established for the particular case of a Pontryagin space ℋ.
9
Content available SOME REMARKS ON GENERALIZED REGRESSION METHODS
100%
Fałda B. , Zając J.
Metody Ilościowe w Badaniach Ekonomicznych
|
2016
|
tom 17
|
nr 4
31-39
EN
As a result of studying certain phenomena gained on the plane, the unit circle and on the earth sphere we present here some introductory notations and remarks, concerning the problems in question.
10
Content available remote Extensions of convex functionals on convex cones
100%
Ignaczak E. , Paszkiewicz A.
Applicationes Mathematicae
|
1998-1999
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tom 25
|
nr 3
381-386
EN
We prove that under some topological assumptions (e.g. if M has nonempty interior in X), a convex cone M in a linear topological space X is a linear subspace if and only if each convex functional on M has a convex extension on the whole space X.
11
Content available remote Singular integral models for p-hyponormal operators and the Riemann-Hilbert problem
100%
Chō M. , Huruya T. , Itoh M.
Studia Mathematica
|
1998
|
tom 130
|
nr 3
213-221
EN
The purpose of this paper is to give singular integral models for p-hyponormal operators and apply them to the Riemann-Hilbert problem.
12
Content available remote Weyl-von Neumann type theorems with the perturbation vanishing on a given subspace, II
88%
Ignaczak E.
|
1998
|
tom Vol. 31, nr 3
529-536
EN
For any (not necessarily orthogonal) projection I in a separable Hilbert space H and for p > 1, epsilon > 0, the perturbation Y is satisfying llYllp < epsilon and 1 + Y being block-diagonal can be taken in such a way that Y P = 0 for any given finite-dimensional orthogonal projection P . II . IIp denotes the Schatten norm.
13
Content available Schauder's fixed-point theorem in approximate controllability problems
88%
Babiarz A. , Klamka J. , Niezabitowski M.
International Journal of Applied Mathematics and Computer Science
|
2016
|
tom 26
|
nr 2
263-275
EN
The main objective of this article is to present the state of the art concerning approximate controllability of dynamic systems in infinite-dimensional spaces. The presented investigation focuses on obtaining sufficient conditions for approximate controllability of various types of dynamic systems using Schauder's fixed-point theorem. We describe the results of approximate controllability for nonlinear impulsive neutral fuzzy stochastic differential equations with nonlocal conditions, impulsive neutral functional evolution integro-differential systems, stochastic impulsive systems with control-dependent coefficients, nonlinear impulsive differential systems, and evolution systems with nonlocal conditions and semilinear evolution equation.
14
Content available remote Computation of reconstruction function for samples in shift-invariant spaces
88%
Zhaoxuan Z. , Houjun W. , Zhigang W.
|
2009
|
tom Vol. 16, nr 4
535-544
EN
We address the problem of reconstructing a class of sampled signals which is a member of shift-invariant spaces. In the traditional method, the reconstruction was obtained by first processing the samples by a digital correction filter, then forming linear combinations of generated functions shifted with period T. In order to eliminate the digital correction filter, we propose a computational approach to the reconstruction function. The reconstruction was directly acquired by forming linear combinations of a set of reconstruction functions. The key idea is to obtain a matrix equation by means of oblique frame theory. The reconstruction functions are obtained by solving the matrix equation. Finally, the computational approach is applied, respectively, to reconstruction of a digitizer which samples the signal by derivative sampling or periodically non-uniform sampling technology. The results show that the method is effective.
15
Content available Existence of solutions for second order stochastic differential inclusions in Hilbert spaces
88%
Balasubramaniam P. , Ntouyas S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2007
|
tom 27
|
nr 2
365-384
EN
In this paper, sufficient conditions are given for the existence of solutions for a class of second order stochastic differential inclusions in Hilbert space with the help of Leray-Schauder Nonlinear Alternative.
16
Content available Measure valued solutions for stochastic evolution equations on Hilbert space and their feedback control
88%
Ahmed N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2005
|
tom 25
|
nr 1
129-157
EN
In this paper, we consider a class of semilinear stochastic evolution equations on Hilbert space driven by a stochastic vector measure. The nonlinear terms are assumed to be merely continuous and bounded on bounded sets. We prove the existence of measure valued solutions generalizing some earlier results of the author. As a corollary, an existence result of a measure solution for a forward Kolmogorov equation with unbounded operator valued coefficients is obtained. The main result is further extended to cover Borel measurable drift and diffusion which are assumed to be bounded on bounded sets. Also we consider control problems for these systems and present several results on the existence of optimal feedback controls.
17
Extending Lipschitz mappings continuously
88%
Kopecka E.
|
|
tom Vol. 18, nr 2
167-177
EN
We consider short mappings from a bounded subset of a Euclidean space into that space, that is, mappings which do not increase distances between points. By Kirszbraun's theorem any such mapping can be extended to the entire space to be short again. In general, the extension is not unique. We show that there are single-valued extension operators continuous in the supremum norm. The multivalued extension operator is lower semicontinuous.
18
Content available remote A class of contractions in Hilbert space and applications
75%
Dungey N.
|
2007
|
tom Vol. 55, no 2
347-355
EN
We characterize the bounded linear operators T in Hilbert space which satisfy T = βI + (1 - β)S where β ∈ (0,1) and S is a contraction. The characterizations include a quadratic form inequality, and a domination condition of the discrete semigroup (T[sup]n)n=1,2,... by the continuous semigroup (e[sup]-t(I-T)t≥o. Moreover, we give a stronger quadratic form inequality which ensures that sup{n||T[sup]n - T[sup]n+1 ||: n = 1, 2,...} < ∞. The results apply to large classes of Markov operators on countable spaces or on locally compact groups.
19
Content available remote Strict pseud-contraction strong convergence theorems for strict pseud-contractions
75%
Qin X. , Su Y.
|
2008
|
tom Vol. 30
137-149
EN
In this paper, we prove two strong convergence theorems for strict pseudocontractions in Hilbert spaces by hybrid methods. Our results extend and improve the recent ones announced by Nakajo and Takahashi [K. Nakajo, W. Takahashi,. Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003), 372-379], Marino and Xu [G. Marino, H.K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007), 336-346], Martinez-Yanes and Xu [C. Martinez-Yanes, H.K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anai. 64 (2006), 2400-2411] and some others.
20
Content available remote Hyperspaces of Peano continua of euclidean spaces
63%
Gladdines H. , van Mill J.
Fundamenta Mathematicae
|
1993
|
tom 142
|
nr 2
173-188
EN
If X is a space then L(X) denotes the subspace of C(X) consisting of all Peano (sub)continua. We prove that for n ≥ 3 the space $L(ℝ^n)$ is homeomorphic to $B^∞$, where B denotes the pseudo-boundary of the Hilbert cube Q.
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