The Experts below are selected from a list of 306 Experts worldwide ranked by ideXlab platform
Hua Zhu - One of the best experts on this subject based on the ideXlab platform.
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Riesz Transform Characterization of Weighted Hardy Spaces Associated with Schrödinger Operators
Journal of Function Spaces, 2016Co-Authors: Hua ZhuAbstract:We characterize the weighted local Hardy spaces related to the critical Radius Function and weights by localized Riesz transforms ; in addition, we give a characterization of weighted Hardy spaces via Riesz transforms associated with Schrodinger operator , where is a Schrodinger operator on () and is a nonnegative Function satisfying the reverse Holder inequality.
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Weighted Weak Local Hardy Spaces Associated with Schrödinger Operators
Journal of Function Spaces, 2015Co-Authors: Hua ZhuAbstract:We characterize the weighted weak local Hardy spaces related to the critical Radius Function and weights which locally behave as Muckenhoupt’s weights and actually include them, by the atomic decomposition. As an application, we show that localized Riesz transforms are bounded on the weighted weak local Hardy spaces.
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Riesz transform characterization of weighted Hardy spaces associated to Schr\"{o}dinger operators
arXiv: Functional Analysis, 2014Co-Authors: Hua ZhuAbstract:In this paper, we characterize the weighted local Hardy spaces $h^p_\rho(\omega)$ related to the critical Radius Function $\rho$ and weights $\omega\in A_{1}^{\rho,\,\infty}(\mathbb{R}^{n})$ by localized Riesz transforms $\widehat{R}_j$, in addition, we give a characterization of weighted Hardy spaces $H^{1}_{\cal L}(\omega)$ via Riesz tranforms associated to Schr\"{o}dinger operator $\cal L$, where $\L=-\Delta+V$ is a Schr\"{o}dinger operator on $\mathbb{R}^{n}$ ($n\ge 3$) and $V$ is a nonnegative Function satisfying the reverse H\"older inequality.
Jae Wook Lee - One of the best experts on this subject based on the ideXlab platform.
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ISNN (1) - Trajectory-Based support vector multicategory classifier
Advances in Neural Networks — ISNN 2005, 2005Co-Authors: Daewon Lee, Jae Wook LeeAbstract:Support vector machines are primarily designed for binary-class classification. Multicategory classification problems are typically solved by combining several binary machines. In this paper, we propose a novel classifier with only one machine for even multiclass data sets. The proposed method consists of two phases. The first phase builds a trained kernel Radius Function via the support vector domain decomposition. The second phase constructs a dynamical system corresponding to the trained kernel Radius Function to decompose data domain and to assign class label to each decomposed domain. Numerical results show that our method is robust and efficient for multicategory classification.
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Trajectory-based support vector multicategory classifier
Lecture Notes in Computer Science, 2005Co-Authors: Daewon Lee, Jae Wook LeeAbstract:Support vector machines are primarily designed for binary-class classification. Multicategory classification problems are typically solved by combining several binary machines. In this paper, we propose a novel classifier with only one machine for even multiclass data sets. The proposed method consists of two phases. The first phase builds a trained kernel Radius Function via the support vector domain decomposition. The second phase constructs a dynamical system corresponding to the trained kernel Radius Function to decompose data domain and to assign class label to each decomposed domain. Numerical results show that our method is robust and efficient for multicategory classification.
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An improved cluster labeling method for support vector clustering
IEEE transactions on pattern analysis and machine intelligence, 2005Co-Authors: Jae Wook Lee, Daewon LeeAbstract:The support vector clustering (SVC) algorithm is a recently emerged unsupervised learning method inspired by support vector machines. One key step involved in the SVC algorithm is the cluster assignment of each data point. A new cluster labeling method for SVC is developed based on some invariant topological properties of a trained kernel Radius Function. Benchmark results show that the proposed method outperforms previously reported labeling techniques.
Daewon Lee - One of the best experts on this subject based on the ideXlab platform.
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ISNN (1) - Trajectory-Based support vector multicategory classifier
Advances in Neural Networks — ISNN 2005, 2005Co-Authors: Daewon Lee, Jae Wook LeeAbstract:Support vector machines are primarily designed for binary-class classification. Multicategory classification problems are typically solved by combining several binary machines. In this paper, we propose a novel classifier with only one machine for even multiclass data sets. The proposed method consists of two phases. The first phase builds a trained kernel Radius Function via the support vector domain decomposition. The second phase constructs a dynamical system corresponding to the trained kernel Radius Function to decompose data domain and to assign class label to each decomposed domain. Numerical results show that our method is robust and efficient for multicategory classification.
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Trajectory-based support vector multicategory classifier
Lecture Notes in Computer Science, 2005Co-Authors: Daewon Lee, Jae Wook LeeAbstract:Support vector machines are primarily designed for binary-class classification. Multicategory classification problems are typically solved by combining several binary machines. In this paper, we propose a novel classifier with only one machine for even multiclass data sets. The proposed method consists of two phases. The first phase builds a trained kernel Radius Function via the support vector domain decomposition. The second phase constructs a dynamical system corresponding to the trained kernel Radius Function to decompose data domain and to assign class label to each decomposed domain. Numerical results show that our method is robust and efficient for multicategory classification.
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An improved cluster labeling method for support vector clustering
IEEE transactions on pattern analysis and machine intelligence, 2005Co-Authors: Jae Wook Lee, Daewon LeeAbstract:The support vector clustering (SVC) algorithm is a recently emerged unsupervised learning method inspired by support vector machines. One key step involved in the SVC algorithm is the cluster assignment of each data point. A new cluster labeling method for SVC is developed based on some invariant topological properties of a trained kernel Radius Function. Benchmark results show that the proposed method outperforms previously reported labeling techniques.
Joao L Costa - One of the best experts on this subject based on the ideXlab platform.
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On the Global Uniqueness for the Einstein–Maxwell-Scalar Field System with a Cosmological Constant
Communications in Mathematical Physics, 2015Co-Authors: Joao L Costa, Pedro M Girao, Jose Natario, Jorge Drumond SilvaAbstract:This paper is the second part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein–Maxwell-scalar field system with a cosmological constant $${\Lambda}$$ Λ , with the data on the outgoing initial null hypersurface given by a subextremal Reissner–Nordström black hole event horizon, study the future extendibility of the corresponding maximal globally hyperbolic development as a “suitably regular” Lorentzian manifold. In the first paper of this sequence (Costa et al., Class Quantum Gravity 32:015017, 2015 ), we established well posedness of the characteristic problem with general initial data. In this second paper, we generalize the results of Dafermos (Ann Math 158:875–928, 2003 ) on the stability of the Radius Function at the Cauchy horizon by including a cosmological constant. This requires a considerable deviation from the strategy followed in Dafermos (Ann Math 158:875–928, 2003 ), focusing on the level sets of the Radius Function instead of the red-shift and blue-shift regions. We also present new results on the global structure of the solution when the free data is not identically zero in a neighborhood of the origin. In the third and final paper (Costa et al., On the global uniqueness for the Einstein–Maxwell-scalar field system with a cosmological constant. Part 3. Mass inflation and extendibility of the solutions. arXiv:1406.7261 , 2015 ), we will consider the issue of mass inflation and extendibility of solutions beyond the Cauchy horizon.
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on the global uniqueness for the einstein maxwell scalar field system with a cosmological constant part 2 structure of the solutions and stability of the cauchy horizon
Communications in Mathematical Physics, 2015Co-Authors: Joao L Costa, Pedro M Girao, Jose Natario, Jorge Drumond SilvaAbstract:This paper is the second part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein–Maxwell-scalar field system with a cosmological constant \({\Lambda}\), with the data on the outgoing initial null hypersurface given by a subextremal Reissner–Nordstrom black hole event horizon, study the future extendibility of the corresponding maximal globally hyperbolic development as a “suitably regular” Lorentzian manifold. In the first paper of this sequence (Costa et al., Class Quantum Gravity 32:015017, 2015), we established well posedness of the characteristic problem with general initial data. In this second paper, we generalize the results of Dafermos (Ann Math 158:875–928, 2003) on the stability of the Radius Function at the Cauchy horizon by including a cosmological constant. This requires a considerable deviation from the strategy followed in Dafermos (Ann Math 158:875–928, 2003), focusing on the level sets of the Radius Function instead of the red-shift and blue-shift regions. We also present new results on the global structure of the solution when the free data is not identically zero in a neighborhood of the origin. In the third and final paper (Costa et al., On the global uniqueness for the Einstein–Maxwell-scalar field system with a cosmological constant. Part 3. Mass inflation and extendibility of the solutions. arXiv:1406.7261, 2015), we will consider the issue of mass inflation and extendibility of solutions beyond the Cauchy horizon.
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on the global uniqueness for the einstein maxwell scalar field system with a cosmological constant part 2 structure of the solutions and stability of the cauchy horizon
arXiv: General Relativity and Quantum Cosmology, 2014Co-Authors: Joao L Costa, Pedro M Girao, Jose Natario, Jorge Drumond SilvaAbstract:This paper is the second part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the outgoing initial null hypersurface given by a subextremal Reissner-Nordstrom black hole event horizon, study the future extendibility of the corresponding maximal globally hyperbolic development as a "suitably regular" Lorentzian manifold. In the first paper of this sequence, we established well posedness of the characteristic problem with general initial data. In this second paper, we generalize the results of Dafermos on the stability of the Radius Function at the Cauchy horizon by including a cosmological constant. This requires a considerable deviation from the strategy followed by Dafermos, focusing on the level sets of the Radius Function instead of the red-shift and blue-shift regions. We also present new results on the global structure of the solution when the free data is not identically zero in a neighborhood of the origin. In the third and final paper, we will consider the issue of mass inflation and extendibility of solutions beyond the Cauchy horizon.
Jorge Drumond Silva - One of the best experts on this subject based on the ideXlab platform.
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On the Global Uniqueness for the Einstein–Maxwell-Scalar Field System with a Cosmological Constant
Communications in Mathematical Physics, 2015Co-Authors: Joao L Costa, Pedro M Girao, Jose Natario, Jorge Drumond SilvaAbstract:This paper is the second part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein–Maxwell-scalar field system with a cosmological constant $${\Lambda}$$ Λ , with the data on the outgoing initial null hypersurface given by a subextremal Reissner–Nordström black hole event horizon, study the future extendibility of the corresponding maximal globally hyperbolic development as a “suitably regular” Lorentzian manifold. In the first paper of this sequence (Costa et al., Class Quantum Gravity 32:015017, 2015 ), we established well posedness of the characteristic problem with general initial data. In this second paper, we generalize the results of Dafermos (Ann Math 158:875–928, 2003 ) on the stability of the Radius Function at the Cauchy horizon by including a cosmological constant. This requires a considerable deviation from the strategy followed in Dafermos (Ann Math 158:875–928, 2003 ), focusing on the level sets of the Radius Function instead of the red-shift and blue-shift regions. We also present new results on the global structure of the solution when the free data is not identically zero in a neighborhood of the origin. In the third and final paper (Costa et al., On the global uniqueness for the Einstein–Maxwell-scalar field system with a cosmological constant. Part 3. Mass inflation and extendibility of the solutions. arXiv:1406.7261 , 2015 ), we will consider the issue of mass inflation and extendibility of solutions beyond the Cauchy horizon.
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on the global uniqueness for the einstein maxwell scalar field system with a cosmological constant part 2 structure of the solutions and stability of the cauchy horizon
Communications in Mathematical Physics, 2015Co-Authors: Joao L Costa, Pedro M Girao, Jose Natario, Jorge Drumond SilvaAbstract:This paper is the second part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein–Maxwell-scalar field system with a cosmological constant \({\Lambda}\), with the data on the outgoing initial null hypersurface given by a subextremal Reissner–Nordstrom black hole event horizon, study the future extendibility of the corresponding maximal globally hyperbolic development as a “suitably regular” Lorentzian manifold. In the first paper of this sequence (Costa et al., Class Quantum Gravity 32:015017, 2015), we established well posedness of the characteristic problem with general initial data. In this second paper, we generalize the results of Dafermos (Ann Math 158:875–928, 2003) on the stability of the Radius Function at the Cauchy horizon by including a cosmological constant. This requires a considerable deviation from the strategy followed in Dafermos (Ann Math 158:875–928, 2003), focusing on the level sets of the Radius Function instead of the red-shift and blue-shift regions. We also present new results on the global structure of the solution when the free data is not identically zero in a neighborhood of the origin. In the third and final paper (Costa et al., On the global uniqueness for the Einstein–Maxwell-scalar field system with a cosmological constant. Part 3. Mass inflation and extendibility of the solutions. arXiv:1406.7261, 2015), we will consider the issue of mass inflation and extendibility of solutions beyond the Cauchy horizon.
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on the global uniqueness for the einstein maxwell scalar field system with a cosmological constant part 2 structure of the solutions and stability of the cauchy horizon
arXiv: General Relativity and Quantum Cosmology, 2014Co-Authors: Joao L Costa, Pedro M Girao, Jose Natario, Jorge Drumond SilvaAbstract:This paper is the second part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the outgoing initial null hypersurface given by a subextremal Reissner-Nordstrom black hole event horizon, study the future extendibility of the corresponding maximal globally hyperbolic development as a "suitably regular" Lorentzian manifold. In the first paper of this sequence, we established well posedness of the characteristic problem with general initial data. In this second paper, we generalize the results of Dafermos on the stability of the Radius Function at the Cauchy horizon by including a cosmological constant. This requires a considerable deviation from the strategy followed by Dafermos, focusing on the level sets of the Radius Function instead of the red-shift and blue-shift regions. We also present new results on the global structure of the solution when the free data is not identically zero in a neighborhood of the origin. In the third and final paper, we will consider the issue of mass inflation and extendibility of solutions beyond the Cauchy horizon.
