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58
Global regularity of the ∂Neumann problem: a survey of the L 2 Sobolev theory, Several Complex Variables
 Partial differential equations in several complex variables, AMS/IP, 2000. Michael Christ, Remarks on global irregularity in the ∂Neumann problem, Several Complex Variables
, 1999
"... 2. The L2 existence theory 1 3. Regularity on general pseudoconvex domains 5 ..."
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Cited by 24 (3 self)
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2. The L2 existence theory 1 3. Regularity on general pseudoconvex domains 5
An explicit description of the reproducing kernel Hilbert spaces of Gaussian RBF kernels
 IEEE Trans. Inform. Theory
, 2005
"... Although Gaussian RBF kernels are one of the most often used kernels in modern machine learning methods such as support vector machines (SVMs), little is known about the structure of their reproducing kernel Hilbert spaces (RKHSs). In this work we give two distinct explicit descriptions of the RKHSs ..."
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Cited by 16 (2 self)
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Although Gaussian RBF kernels are one of the most often used kernels in modern machine learning methods such as support vector machines (SVMs), little is known about the structure of their reproducing kernel Hilbert spaces (RKHSs). In this work we give two distinct explicit descriptions of the RKHSs corresponding to Gaussian RBF kernels and discuss some consequences. Furthermore, we present an orthonormal system for these spaces. Finally we discuss how our results can be used for analyzing the learning performance of SVMs.
Capacityachieving probability measure for conditionally Gaussian channels with bounded inputs
 IEEE Trans. Inf. Theory
, 2005
"... Abstract—A conditionally Gaussian channel is a vector channel in which the channel output, given the channel input, has a Gaussian distribution with (wellbehaved) inputdependent mean and covariance. We study the capacityachieving probability measure for conditionally Gaussian channels subject to ..."
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Cited by 15 (0 self)
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Abstract—A conditionally Gaussian channel is a vector channel in which the channel output, given the channel input, has a Gaussian distribution with (wellbehaved) inputdependent mean and covariance. We study the capacityachieving probability measure for conditionally Gaussian channels subject to boundedinput constraints and average cost constraints. Many practical communication systems, including additive Gaussian noise channels, certain optical channels, fading channels, and interference channels fall within this framework. Subject to boundedinput constraint (and average cost constraints), we show that the channel capacity is achievable and we derive a necessary and sufficient condition for a probability measure to be capacity achieving. Under certain conditions, the capacityachieving measure is proved to be discrete. Index Terms—Boundedinput constraint, capacityachieving measure, conditionally Gaussian channel, optical channel,
Holomorphic curves in complex spaces
, 2006
"... Abstract. We study the existence of closed complex curves normalized by bordered Riemann surfaces in complex spaces. Our main result is that such curves abound in any non compact complex space admitting an exhaustion function whose Levi form has at least two positive eigenvalues at every point outsi ..."
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Cited by 12 (4 self)
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Abstract. We study the existence of closed complex curves normalized by bordered Riemann surfaces in complex spaces. Our main result is that such curves abound in any non compact complex space admitting an exhaustion function whose Levi form has at least two positive eigenvalues at every point outside a compact set, and this condition is essential. We also construct a Stein neighborhood basis of any compact complex curve with C 2 boundary in a complex space. 1.
Sparseness of support vector machines  Some asymptotically sharp bounds
 ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 16
, 2004
"... The decision functions constructed by support vector machines (SVM’s) usually depend only on a subset of the training set—the socalled support vectors. We derive asymptotically sharp lower and upper bounds on the number of support vectors for several standard types of SVM’s. Our results significant ..."
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Cited by 11 (1 self)
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The decision functions constructed by support vector machines (SVM’s) usually depend only on a subset of the training set—the socalled support vectors. We derive asymptotically sharp lower and upper bounds on the number of support vectors for several standard types of SVM’s. Our results significantly improve recent achievments of the author.
A New Approach for Analysis and Synthesis of TimeVarying Systems
, 1997
"... In this paper new techniques are developed for the analysis of linear time varying (LTV) systems. These lead to a formally simple treatment of problems for LTV systems, allowing methods more usually restricted to timeinvariant systems to be employed in the timevarying case. As an illustration of th ..."
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Cited by 8 (3 self)
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In this paper new techniques are developed for the analysis of linear time varying (LTV) systems. These lead to a formally simple treatment of problems for LTV systems, allowing methods more usually restricted to timeinvariant systems to be employed in the timevarying case. As an illustration of this methodology, the socalled H1 synthesis problem is solved for linear timevarying systems. 1 Introduction In this paper, new techniques are developed for the analysis of linear time varying (LTV) systems. These lead to a formally simple treatment of problems for LTV systems, allowing methods more usually restricted to timeinvariant systems to be employed in the timevarying case. As an example of this methodology, the socalled H1 synthesis problem is solved for linear timevarying systems. The main idea of the paper is that the usual state space description of a linear timevarying (LTV) system x k+1 = A k x k +B k u k y k = C k x k +D k u k described by time varying matrices A, B,...
The Hartogs extension theorem on (n − 1)complete complex spaces, available at http://www.arxiv.org
"... ABSTRACT. Employing Morse theory and the method of analytic discs but no ∂ techniques, we establish a version of the Hartogs extension theorem in a singular setting, namely: for every domain Ω of an (n − 1)complete normal complex space of pure dimension n � 2, and for every compact set K ⊂ Ω such th ..."
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Cited by 7 (1 self)
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ABSTRACT. Employing Morse theory and the method of analytic discs but no ∂ techniques, we establish a version of the Hartogs extension theorem in a singular setting, namely: for every domain Ω of an (n − 1)complete normal complex space of pure dimension n � 2, and for every compact set K ⊂ Ω such that Ω\K is connected, holomorphic or meromorphic functions in Ω\K extend holomorphically or meromorphically to Ω.
Majorant Series
, 2000
"... This article discusses questions in one and several complex variables about the size of the sum of the moduli of the terms of the series expansion of a bounded holomorphic function. Although the article is partly expository, it also includes some previously unpublished results with complete proofs. ..."
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Cited by 7 (0 self)
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This article discusses questions in one and several complex variables about the size of the sum of the moduli of the terms of the series expansion of a bounded holomorphic function. Although the article is partly expository, it also includes some previously unpublished results with complete proofs. 1.
On Equivalence of Two Constructions of Invariants of Lagrangian Submanifolds
 Pacific J. Math
"... We give the construction ofsymplectic invariants which incorporates both the “infinite dimensional ” invariants constructed by Oh in 1997 and the “finite dimensional ” ones constructed by Viterbo in 1992. 1. Introduction. Let M be a compact smooth manifold. Its cotangent bundle T ∗M carries a natura ..."
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Cited by 7 (0 self)
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We give the construction ofsymplectic invariants which incorporates both the “infinite dimensional ” invariants constructed by Oh in 1997 and the “finite dimensional ” ones constructed by Viterbo in 1992. 1. Introduction. Let M be a compact smooth manifold. Its cotangent bundle T ∗M carries a natural symplectic structure associated to a Liouville form θ = pdq. For a given compactly supported Hamiltonian function H: T ∗M → R and a closed submanifold N ⊂ M Oh [30, 27] defined a symplectic invariants of
Proving a manifold to be hyperbolic once it has been approximated to be so
, 2004
"... This paper presents the major result of my doctoral dissertation written at Columbia University [11], with Walter Neumann as my thesis adviser. Known uses of the method ..."
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Cited by 6 (0 self)
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This paper presents the major result of my doctoral dissertation written at Columbia University [11], with Walter Neumann as my thesis adviser. Known uses of the method