2. The L2 existence theory 1 3. Regularity on general pseudoconvex domains 5

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.

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

The decision functions constructed by support vector machines (SVM’s) usually depend only on a subset of the training set—the so-called 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.

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 time-invariant systems to be employed in the timevarying case. As an illustration of this methodology, the so-called H1 synthesis problem is solved for linear time-varying 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 time-varying case. As an example of this methodology, the so-called H1 synthesis problem is solved for linear time-varying systems. The main idea of the paper is that the usual state space description of a linear time-varying (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,...

We prove that there is a universal measure on the unit circle such that any probability measure on the unit disk is the limit distribution of some subsequence of the corresponding orthogonal polynomials. This follows from an extension of a result of Alfaro and Vigil (which answered a question of P. Turán): namely, for n < N, one can freely prescribe the n-th polynomial and N − n zeros of the N-th one. We shall also describe all possible limit sets of zeros within the unit disk. 1

Abstract. Boas ’ characterization of bounded domains for which the Bochner-Martinelli kernel is self-adjoint is extended to the case of a weighted measure. For strictly convex domains, this equivalently characterizes the ones whose Leray-Aǐzenberg kernel is self-adjoint with respect to weighted measure. In each case, the domains are complex linear images of a ball, and the measure is the Fefferman measure. The Leray-Aǐzenberg kernel for a strictly convex hypersurface in C n is shown to be Möbius invariant when defined with respect to Fefferman measure. 1.

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.

Suppose r is a defining function for a twice differentiable hypersurface M 2n−1 ⊂ Cn near p ∈ M. In complex form, the Taylor expansion for r is given by n ∑ ∂r

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