The Experts below are selected from a list of 32763 Experts worldwide ranked by ideXlab platform
Silviu Urziceanu - One of the best experts on this subject based on the ideXlab platform.
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The canonical projection associated with certain possibly infinite generalized iterated function systems as a fixed point
Journal of Fixed Point Theory and Applications, 2018Co-Authors: Radu Miculescu, Silviu UrziceanuAbstract:In this paper, influenced by the ideas from Mihail (Fixed Point Theory Appl 2015:15, 2015), we associate to every generalized iterated function system $$\mathcal {F}$$ (of order m) an operator $$H_{\mathcal {F}}:\mathcal {C} ^{m}\rightarrow \mathcal {C}$$ , where $$\mathcal {C}$$ stands for the space of continuous functions from the shift space on the metric space corresponding to the system. We provide Sufficient Conditions (on the constitutive functions of $$\mathcal {F}$$ ) for the operator $$H_{\mathcal {F}}$$ to be continuous, contraction, $$\varphi $$ -contraction, Meir–Keeler or contractive. We also Give Sufficient Condition under which $$H_{\mathcal {F}}$$ has a unique fixed point $$\pi _{0}$$ . Moreover, we prove that, under these circumstances, the closure of the imagine of $$\pi _{0}$$ is the attractor of $$\mathcal {F}$$ and that $$\pi _{0}$$ is the canonical projection associated with $$\mathcal {F}$$ . In this way we Give a partial answer to the open problem raised on the last paragraph of the above-mentioned Mihail’s paper.
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The canonical projection associated to certain possibly infinite generalized iterated function system as a fixed point
arXiv: Classical Analysis and ODEs, 2018Co-Authors: Radu Miculescu, Silviu UrziceanuAbstract:In this paper, influenced by the ideas from A. Mihail, The canonical projection between the shift space of an IIFS and its attractor as a fixed point, Fixed Point Theory Appl., 2015, Paper No. 75, 15 p., we associate to every generalized iterated function system F (of order m) an operator H defined on C^m and taking values on C, where C stands for the space of continuous functions from the shift space on the metric space corresponding to the system. We provide Sufficient Conditions (on the constitutive functions of F) for the operator H to be continuous, contraction, phi-contraction, Meir-Keeler or contractive. We also Give Sufficient Condition under which H has a unique fixed point. Moreover, we prove that, under these circumstances, the closer of the imagine of the fixed point is the attractor of F and that the fixed point is the canonical projection associated to F. In this way we Give a partial answer to the open problem raised on the last paragraph of the above mentioned Mihail's paper.
Radu Miculescu - One of the best experts on this subject based on the ideXlab platform.
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The canonical projection associated with certain possibly infinite generalized iterated function systems as a fixed point
Journal of Fixed Point Theory and Applications, 2018Co-Authors: Radu Miculescu, Silviu UrziceanuAbstract:In this paper, influenced by the ideas from Mihail (Fixed Point Theory Appl 2015:15, 2015), we associate to every generalized iterated function system $$\mathcal {F}$$ (of order m) an operator $$H_{\mathcal {F}}:\mathcal {C} ^{m}\rightarrow \mathcal {C}$$ , where $$\mathcal {C}$$ stands for the space of continuous functions from the shift space on the metric space corresponding to the system. We provide Sufficient Conditions (on the constitutive functions of $$\mathcal {F}$$ ) for the operator $$H_{\mathcal {F}}$$ to be continuous, contraction, $$\varphi $$ -contraction, Meir–Keeler or contractive. We also Give Sufficient Condition under which $$H_{\mathcal {F}}$$ has a unique fixed point $$\pi _{0}$$ . Moreover, we prove that, under these circumstances, the closure of the imagine of $$\pi _{0}$$ is the attractor of $$\mathcal {F}$$ and that $$\pi _{0}$$ is the canonical projection associated with $$\mathcal {F}$$ . In this way we Give a partial answer to the open problem raised on the last paragraph of the above-mentioned Mihail’s paper.
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The canonical projection associated to certain possibly infinite generalized iterated function system as a fixed point
arXiv: Classical Analysis and ODEs, 2018Co-Authors: Radu Miculescu, Silviu UrziceanuAbstract:In this paper, influenced by the ideas from A. Mihail, The canonical projection between the shift space of an IIFS and its attractor as a fixed point, Fixed Point Theory Appl., 2015, Paper No. 75, 15 p., we associate to every generalized iterated function system F (of order m) an operator H defined on C^m and taking values on C, where C stands for the space of continuous functions from the shift space on the metric space corresponding to the system. We provide Sufficient Conditions (on the constitutive functions of F) for the operator H to be continuous, contraction, phi-contraction, Meir-Keeler or contractive. We also Give Sufficient Condition under which H has a unique fixed point. Moreover, we prove that, under these circumstances, the closer of the imagine of the fixed point is the attractor of F and that the fixed point is the canonical projection associated to F. In this way we Give a partial answer to the open problem raised on the last paragraph of the above mentioned Mihail's paper.
Hafida Laasri - One of the best experts on this subject based on the ideXlab platform.
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Well-posedness of infinite-dimensional non-autonomous passive boundary control systems
arXiv: Functional Analysis, 2019Co-Authors: Birgit Jacob, Hafida LaasriAbstract:We study a class of non-autonomous boundary control and observation linear systems that are governed by non-autonomous multiplicative perturbations. This class is motivated by different fundamental partial differential equations, such as controlled wave equations and Timoshenko beams. Our main results Give Sufficient Condition for well-posedness, existence and uniqueness of classical and mild solutions.
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Well-posedness of infinite-dimensional non-autonomous passive boundary control systems
Evolution Equations & Control Theory, 2019Co-Authors: Birgit Jacob, Hafida LaasriAbstract:We study a class of non-autonomous linear boundary control and observation systems that are governed by non-autonomous multiplicative perturbations. This class is motivated by fundamental partial differential equations, such as controlled wave equations and Timoshenko beams. Our main results Give Sufficient Condition for well-posedness, existence and uniqueness of classical and mild solutions.
Birgit Jacob - One of the best experts on this subject based on the ideXlab platform.
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Well-posedness of infinite-dimensional non-autonomous passive boundary control systems
arXiv: Functional Analysis, 2019Co-Authors: Birgit Jacob, Hafida LaasriAbstract:We study a class of non-autonomous boundary control and observation linear systems that are governed by non-autonomous multiplicative perturbations. This class is motivated by different fundamental partial differential equations, such as controlled wave equations and Timoshenko beams. Our main results Give Sufficient Condition for well-posedness, existence and uniqueness of classical and mild solutions.
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Well-posedness of infinite-dimensional non-autonomous passive boundary control systems
Evolution Equations & Control Theory, 2019Co-Authors: Birgit Jacob, Hafida LaasriAbstract:We study a class of non-autonomous linear boundary control and observation systems that are governed by non-autonomous multiplicative perturbations. This class is motivated by fundamental partial differential equations, such as controlled wave equations and Timoshenko beams. Our main results Give Sufficient Condition for well-posedness, existence and uniqueness of classical and mild solutions.
Yanqi Qiu - One of the best experts on this subject based on the ideXlab platform.
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Linear rigidity of stationary stochastic processes
Ergodic Theory and Dynamical Systems, 2018Co-Authors: Alexander I. Bufetov, Yoann Dabrowski, Yanqi QiuAbstract:We consider stationary stochastic processes $\{X_n : n \in Z\}$ such that $X_0$ lies in the closed linear span of $\{X_n : n = 0\}$; following Ghosh and Peres, we call such processes linearly rigid. Using a criterion of Kolmogorov, we show that it suffices, for a stationary stochastic process to be linearly rigid, that the spectral density vanish at zero and belong to the Zygmund class $\Gamma^*(1)$. We next Give Sufficient Condition for stationary determinantal point processes on $\mathbb{Z}$ and on $\mathbb{R}$ to be linearly rigid. Finally, we show that the determinantal point process on $\mathbb{R}^2$ induced by a tensor square of Dyson sine-kernels is not linearly rigid.
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Linear rigidity of stationary stochastic processes
2016Co-Authors: Alexander I. Bufetov, Yoann Dabrowski, Yanqi QiuAbstract:We consider stationary stochastic processes X n , n ∈ Z such that X 0 lies in the closed linear span of X n , n = 0; following Ghosh and Peres, we call such processes linearly rigid. Using a criterion of Kolmogorov, we show that it suffices, for a stationary stochastic process to be rigid, that the spectral density vanish at zero and belong to the Zygmund class Λ * (1). We next Give Sufficient Condition for stationary determinantal point processes on Z and on R to be rigid. Finally, we show that the determinantal point process on R 2 induced by a tensor square of Dyson sine-kernels is not linearly rigid.