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Tytuł:
Well-posedness and stability analysis of hybrid feedback systems using Shkalikovs theory
Autorzy:
Grabowski, P.
Powiązania:
https://bibliotekanauki.pl/articles/254925.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
infinite-dimensional control systems
semigroups
spectral methods
Riesz bases
Opis:
The modern method of analysis of the distributed parameter systems relies on the transformation of the dynamical model to an abstract differential equation on an appropriately chosen Banach or, if possible, Hilbert space. A linear dynamical model in the form of a first order abstract differential equation is considered to be well-posed if its right-hand side generates a strongly continuous semigroup. Similarly, a dynamical model in the form of a second order abstract differential equation is well-posed if its right-hand side generates a strongly continuous cosine family of operators. Unfortunately, the presence of a feedback leads to serious complications or even excludes a direct verification of assumptions of the Hille-Phillips-Yosida and/or the Sova-Fattorini Theorems. The class of operators which are similar to a normal discrete operator on a Hilbert space describes a wide variety of linear operators. In the papers [12, 13] two groups of similarity criteria for a given hybrid closed-loop system operator are given. The criteria of the first group are based on some perturbation results, and of the second, on the application of Shkalikov's theory of the Sturm-Liouville eigenproblems with a spectral parameter in the boundary conditions. In the present paper we continue those investigations showing certain advanced applications of the Shkalikov's theory. The results are illustrated by feedback control systems examples governed by wave and beam equations with increasing degree of complexity of the boundary conditions.
Źródło:
Opuscula Mathematica; 2006, 26, 1; 45-97
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Vector series whose lacunary subseries converge
Autorzy:
Drewnowski, Lech
Labuda, Iwo
Powiązania:
https://bibliotekanauki.pl/articles/1206244.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
subseries convergence
lacunary subseries
zero-density subseries
lacunary convergence property
topological Riesz space of measurable functions
topological vector space of Bochner measurable functions
Lebesgue property
Levi property
copy of $c_0$
Opis:
The area of research of this paper goes back to a 1930 result of H. Auerbach showing that a scalar series is (absolutely) convergent if all its zero-density subseries converge. A series $∑_n x_n$ in a topological vector space X is called ℒ-convergent if each of its lacunary subseries $∑_k x_{n_k}$ (i.e. those with $n_{k+1} - n_k → ∞$) converges. The space X is said to have the Lacunary Convergence Property, or LCP, if every ℒ-convergent series in X is convergent; in fact, it is then subseries convergent. The Zero-Density Convergence Property, or ZCP, is defined similarly though of lesser importance here. It is shown that for every ℒ-convergent series the set of all its finite sums is metrically bounded; however, it need not be topologically bounded. Next, a space with the LCP contains no copy of the space $c_0$. The converse holds for Banach spaces and, more generally, sequentially complete locally pseudoconvex spaces. However, an F-lattice of measurable functions is constructed that has both the Lebesgue and Levi properties, and thus contains no copy of $c_0$, and, nonetheless, lacks the LCP. The main (and most difficult) result of the paper is that if a Banach space E contains no copy of $c_0$ and λ is a finite measure, then the Bochner space $L_0$ (λ,e) has the LCP. From this, with the help of some Orlicz-Pettis type theorems proved earlier by the authors, the LCP is deduced for a vast class of spaces of (scalar and vector) measurable functions that have the Lebesgue type property and are "metrically-boundedly sequentially closed" in the containing $L_0$ space. Analogous results about the convergence of ℒ-convergent positive series in topological Riesz spaces are also obtained. Finally, while the LCP implies the ZCP trivially, an example is given that the converse is false, in general.
Źródło:
Studia Mathematica; 2000, 138, 1; 53-80
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The motion planning problem and exponential stabilization of a heavy chain. Part II
Autorzy:
Grabowski, P.
Powiązania:
https://bibliotekanauki.pl/articles/255394.pdf
Data publikacji:
2008
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
infinite-dimensional control systems
semigroups
motion planning problem
exponential stabilization
spectral methods
Riesz bases
exact observability
Opis:
This is the second part of paper [8], where a model of a heavy chain system with a punctual load (tip mass) in the form of a system of partial differential equations was interpreted as an abstract semigroup system and then analysed on a Hilbert state space. In particular, in [8] we have formulated the problem of exponential stabilizability of a heavy chain in a given position. It was also shown that the exponential stability can be achieved by applying a stabilizer of the colocated-type. The proof used the method of Lyapunov functionals. In the present paper, we give other two proofs of the exponential stability, which provides an additional intrinsic insight into the exponential stabilizability mechanism. The first proof makes use of some spectral properties of the system. In the second proof, we employ some relationships between exponential stability and exact observability.
Źródło:
Opuscula Mathematica; 2008, 28, 4; 481-505
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Fejer-Riesz type result for some weighted Hilbert spaces of analytic functions in the unit disc
Autorzy:
Jakóbczak, P.
Powiązania:
https://bibliotekanauki.pl/articles/254853.pdf
Data publikacji:
2011
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Fejer-Riesz inequality
Hilbert spaces of analytic functions
Opis:
In this note we prove Fejer-Riesz inequality type results for some weighted Hilbert spaces of analytic functions in the unit disc. We describe also a class of such spaces for which Fejer-Riesz inequality type results do not hold.
Źródło:
Opuscula Mathematica; 2011, 31, 4; 605-614
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The basis property of eigenfunctions in the problem of a nonhomogeneous damped string
Autorzy:
Rzepnicki, Ł.
Powiązania:
https://bibliotekanauki.pl/articles/254937.pdf
Data publikacji:
2017
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
nonhomogeneous damped string
Hilbert space
Riesz basis
modulus of continuity
basis with parentheses
string equation
Opis:
The equation which describes the small vibrations of a nonhomogeneous damped string can be rewritten as an abstract Cauchy problem for the densely defined closed operator iA. We prove that the set of root vectors of the operator A forms a basis of subspaces in a certain Hilbert space H. Furthermore, we give the rate of convergence for the decomposition with respect to this basis. In the second main result we show that with additional assumptions the set of root vectors of the operator A is a Riesz basis for H.
Źródło:
Opuscula Mathematica; 2017, 37, 1; 141-165
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sur les dimensions de mesures
Autorzy:
Hua Fan, Ai
Powiązania:
https://bibliotekanauki.pl/articles/1290182.pdf
Data publikacji:
1994
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
upper and lower dimension
dimension formulas
unidimensional
multifractal
Gibbs measure
Markov measure
Riesz product
Opis:
Firstly, we introduce the lower and upper dimensions for a measure defined on a metric space. Secondly, we establish the dimension formulas and characterize the unidimensional measures which were introduced by J.-P. Kahane. Lastly, we give some applications of these to the calculus of dimensions and the multifractal analysis of certain well known measures such as Lebesgue measures on Cantor sets, Gibbs measures, Markov measures and Riesz products etc.
Źródło:
Studia Mathematica; 1994, 111, 1; 1-17
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sturm-Liouville Systems Are Riesz-Spectral Systems
Autorzy:
Delattre, C.
Dochain, D.
Winkin, J.
Powiązania:
https://bibliotekanauki.pl/articles/908100.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
matematyka
Sturm-Liouville system
Riesz-spectral system
infinite-dimensional state-space system
Co-semigroup
Opis:
The class of Sturm-Liouville systems is defined. It appears to be a subclass of Riesz-spectral systems, since it is shown that the negative of a Sturm-Liouville operator is a Riesz-spectral operator on L2(a,b) and the infinitesimal generator of a C0-semigroup of bounded linear operators.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2003, 13, 4; 481-484
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some remarks on spectral approximation for compact operators
Autorzy:
Moszyński, K.
Pokrzywa, A.
Powiązania:
https://bibliotekanauki.pl/articles/747559.pdf
Data publikacji:
1978
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Compact operators,Riesz operators,quations and inequalities involving linear operators, with vector unknowns,Equations with linear operators
Opis:
Artykuł nie zawiera streszczenia
Finite-dimensional approximations for linear compact operators are constructed by discretization of the underlying Banach space. Sufficient conditions for strong convergence of the finite-dimensional operators to the given compact operator and for their collective compactness are obtained. In particular, the finite-dimensional approximation of the pencil A−λJ:H→V is considered, where H,V are Banach spaces, A is an invertible and J a compact operator.
Źródło:
Mathematica Applicanda; 1978, 6, 12
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some remarks on Bochner-Riesz means
Autorzy:
Thangavelu, S.
Powiązania:
https://bibliotekanauki.pl/articles/965807.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
unitary representations
Schrödinger operators
Bochner-Riesz means
nilpotent groups
Rockland operators
Heisenberg group
summability
Opis:
We study $L^p$ norm convergence of Bochner-Riesz means $S_R^δ f$ associated with certain non-negative differential operators. When the kernel $S_R^m(x,y)$ satisfies a weak estimate for large values of m we prove $L^p$ norm convergence of $S_R^δ f$ for δ > n|1/p-1/2|, 1 < p < ∞, where n is the dimension of the underlying manifold.
Źródło:
Colloquium Mathematicum; 2000, 83, 2; 217-230
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sidon sets and Riesz sets for some measure algebras on the disk
Autorzy:
Gebuhrer, Olivier
Schwartz, Alan
Powiązania:
https://bibliotekanauki.pl/articles/966664.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
disk polynomials
bivariate polynomials
Riesz sets
hypergroups
Sidon sets
Opis:
Sidon sets for the disk polynomial measure algebra (the continuous disk polynomial hypergroup) are described completely in terms of classical Sidon sets for the circle; an analogue of the F. and M. Riesz theorem is also proved.
Źródło:
Colloquium Mathematicum; 1997, 72, 2; 269-279
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Seminormal systems of operators in Clifford environments
Autorzy:
Mircea, M.
Powiązania:
https://bibliotekanauki.pl/articles/255159.pdf
Data publikacji:
2017
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
multidimensional operator theory
joint seminormality
Riesz transforms
Putnam inequality
Opis:
The primary goal of our article is to implement some standard spin geometry techniques related to the study of Dirac and Laplace operators on Dirac vector bundles into the multidimensional theory of Hilbert space operators. The transition from spin geometry to operator theory relies on the use of Clifford environments, which essentially are Clifford algebra augmentations of unital complex C*-algebras that enable one to set up counterparts of the geometric Bochner-Weitzenbock and Bochner-Kodaira-Nakano curvature identities for systems of elements of a C*-algebra. The so derived self-commutator identities in conjunction with Bochner’s method provide a natural motivation for the definitions of several types of seminormal systems of operators. As part of their study, we single out certain spectral properties, introduce and analyze a singular integral model that involves Riesz transforms, and prove some self-commutator inequalities.
Źródło:
Opuscula Mathematica; 2017, 37, 1; 81-107
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Riesz-Laplace Wavelet Transform and PCNN Based Image Fusion
Autorzy:
Sun, Shuifa
Tang, Yongheng
Mei, Zhoujunshen
Yang, Min
Tang, Tinglong
Wu, Yirong
Powiązania:
https://bibliotekanauki.pl/articles/2204258.pdf
Data publikacji:
2023
Wydawca:
Szkoła Główna Gospodarstwa Wiejskiego w Warszawie. Instytut Informatyki Technicznej
Tematy:
image fusion
Riesz transforms
polyharmonic spline
Laplacian wavelet
pulse-coupled neural networks
PCNN
Opis:
Important information perceived by human vision comes from the low-level features of the image, which can be extracted by the Riesz transform. In this study, we propose a Riesz transform based approach to image fusion. The image to be fused is first decomposed using the Riesz transform. Then the image sequence obtained in the Riesz transform domain is subjected to the Laplacian wavelet transform based on the fractional Laplacian operators and the multi-harmonic splines. After Laplacian wavelet transform, the image representations have directional and multi-resolution characteristics. Finally, image fusion is performed, leveraging Riesz-Laplace wavelet analysis and the global coupling characteristics of pulse coupled neural network (PCNN). The proposed approach has been tested in several application scenarios, such as multi-focus imaging, medical imaging, remote sensing full-color imaging, and multi-spectral imaging. Compared with conventional methods, the proposed approach demonstrates superior performance on visual effects, contrast, clarity, and the overall efficiency.
Źródło:
Machine Graphics & Vision; 2023, 32, 1; 73--84
1230-0535
2720-250X
Pojawia się w:
Machine Graphics & Vision
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Riesz triple probabilisitic of almost lacunary Cesáro C111 statistical convergence of Γ3 defined by a Musielak Orlicz function
Autorzy:
Esi, Ayhan
Subramanian, Nagarajan
Ozdemir, M. Kemal
Powiązania:
https://bibliotekanauki.pl/articles/1076148.pdf
Data publikacji:
2019
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Cesáro C111 - statistical convergence
Orlicz function
Riesz space
analytic sequence
entire sequence
statistical convergence
triple sequences
Opis:
In this paper we study the concept of almost lacunary statistical Cesáro of Γ3 over probabilistic p- metric spaces defined by Musielak Orlicz function. Since the study of convergence in PP-spaces is fundamental to probabilistic functional analysis, we feel that the concept of almost lacunary statistical Cesáro of Γ3 over probabilistic p- metric spaces defined by Musielak in a PP-space would provide a more general framework for the subject.
Źródło:
World Scientific News; 2019, 116; 115-127
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Riesz means of Fourier transforms and Fourier series on Hardy spaces
Autorzy:
Weisz, Ferenc
Powiązania:
https://bibliotekanauki.pl/articles/1217804.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Hardy spaces
p-atom
atomic decomposition
interpolation
Fourier transforms
Riesz means
Opis:
Elementary estimates for the Riesz kernel and for its derivative are given. Using these we show that the maximal operator of the Riesz means of a tempered distribution is bounded from $H_p(ℝ)$ to $L_p(ℝ)$ (1/(α+1) < p < ∞) and is of weak type (1,1), where $H_p(ℝ)$ is the classical Hardy space. As a consequence we deduce that the Riesz means of a function $⨍ ∈ L_1(ℝ)$ converge a.e. to ⨍. Moreover, we prove that the Riesz means are uniformly bounded on $H_p(ℝ)$ whenever 1/(α+1) < p < ∞. Thus, in case $⨍ ∈ H_p(ℝ)$, the Riesz means converge to ⨍ in $H_p(ℝ)$ norm (1/(α+1) < p < ∞). The same results are proved for the conjugate Riesz means and for Fourier series of distributions.
Źródło:
Studia Mathematica; 1998, 131, 3; 253-270
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On uniqueness of G-measures and g-measures
Autorzy:
Hua Fan, Ai
Powiązania:
https://bibliotekanauki.pl/articles/1287544.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
G-measures
g-measures
ergodic measures
Riesz products
quasi-invariance
dimension of measures
Opis:
We give a simple proof of the sufficiency of a log-lipschitzian condition for the uniqueness of G-measures and g-measures which were studied by G. Brown, A. H. Dooley and M. Keane. In the opposite direction, we show that the lipschitzian condition together with positivity is not sufficient. In the special case where the defining function depends only upon two coordinates, we find a necessary and sufficient condition. The special case of Riesz products is discussed and the Hausdorff dimension of Riesz products is calculated.
Źródło:
Studia Mathematica; 1996, 119, 3; 255-269
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 40

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