Results 41 to 50 of about 63,696 (324)
Reproducing Kernels and Discretization
, 2015 We give a short survey of a general discretization method based on the theory of reproducing kernels. We believe our method will become the next generation method for solving analytical problems by computers. For example, for solving linear PDEs with general boundary or initial value conditions, independently of the domains.
Castro, L. P. +4 more
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Subgroups of Paths and Reproducing Kernels [PDF]
The Annals of Probability, 1973 The following generalizations of certain theorems due to G. Kallianpur and to Jamison and Orey are proved for an arbitrary Gaussian measure $P$ on a space of real functions: if the reproducing kernel Hilbert space $H$ is infinite dimensional then $P(H) = 0$; if a subgroup $G$ of the space of real functions (under addition) is measurable with respect to
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On functional reproducing kernels
Open Mathematics, 2023 Abstract We show that even if a Hilbert space does not admit a reproducing kernel, there could still be a kernel function that realizes the Riesz representation map. Constructions in spaces that are the Fourier transform of weighted
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Factorizations of Kernels and Reproducing Kernel Hilbert Spaces [PDF]
Integral Equations and Operator Theory, 2017 The paper discusses a series of results concerning reproducing kernel Hilbert spaces, related to the factorization of their kernels. In particular, it is proved that for a large class of spaces isometric multipliers are trivial. One also gives for certain spaces conditions for obtaining a particular type of dilation, as well as a classification of ...
Dan Timotin +3 more
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A Quasi-Convex RKPM for 3D Steady-State Thermomechanical Coupling Problems
MathematicsA meshless, quasi-convex reproducing kernel particle framework for three-dimensional steady-state thermomechanical coupling problems is presented in this paper.
Lin Zhang +3 more
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Solving a System of Linear Volterra Integral Equations Using the Modified Reproducing Kernel Method
Abstract and Applied Analysis, 2013 A numerical technique based on reproducing kernel methods for the exact solution of linear Volterra integral equations system of the second kind is given.
Li-Hong Yang +2 more
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Reproducing Kernel Method with Global Derivative
Journal of Function Spaces, 2023 Ordinary differential equations describe several phenomena in different fields of engineering and physics. Our aim is to use the reproducing kernel Hilbert space method (RKHSM) to find a solution to some ordinary differential equations (ODEs) that are ...
Nourhane Attia +2 more
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Analysis of unbounded operators and random motion
, 2009 We study infinite weighted graphs with view to \textquotedblleft limits at infinity,\textquotedblright or boundaries at infinity. Examples of such weighted graphs arise in infinite (in practice, that means \textquotedblleft very\textquotedblright large ...
Dunford N. +6 more
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Radial kernels and their reproducing kernel Hilbert spaces [PDF]
Journal of Complexity, 2010 AbstractWe describe how to use Schoenberg’s theorem for a radial kernel combined with existing bounds on the approximation error functions for Gaussian kernels to obtain a bound on the approximation error function for the radial kernel. The result is applied to the exponential kernel and Student’s kernel. To establish these results we develop a general
Ingo Steinwart +3 more
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Branching problems in reproducing kernel spaces [PDF]
Duke Mathematical Journal, 2020 For a semisimple Lie group $G$ satisfying the equal rank condition, the most basic family of unitary irreducible representations is the discrete series found by Harish-Chandra. In this paper, we study some of the branching laws for discrete series when restricted to a subgroup $H$ of the same type by combining classical results with recent work of T ...
Ørsted, Bent, Vargas, Jorge A.
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