New characterizations of reproducing kernel Hilbert spaces and applications to metric geometry [PDF]
Opuscula Mathematica, 2021 We give two new global and algorithmic constructions of the reproducing kernel Hilbert space associated to a positive definite kernel. We further present a general positive definite kernel setting using bilinear forms, and we provide new examples.
Daniel Alpay, Palle E.T. Jorgensen
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New Reproducing Kernel Functions [PDF]
Mathematical Problems in Engineering, 2015 Some new reproducing kernel functions on time scales are presented. Reproducing kernel functions have not been found on time scales till now. These functions are very important on time scales and they will be very useful for researchers. We need these functions to solve dynamic equations on time scales with the reproducing kernel method.
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Theory of Reproducing Kernels [PDF]
Transactions of the American Mathematical Society, 1950 Abstract : The present paper may be considered as a sequel to our previous paper in the Proceedings of the Cambridge Philosophical Society, Theorie generale de noyaux reproduisants-Premiere partie (vol. 39 (1944)) which was written in 1942-1943. In the introduction to this paper we outlined the plan of papers which were to follow.
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Representations of $*$-semigroups associated to invariant kernels with values adjointable operators. I [PDF]
, 2015 We consider positive semidefinite kernels valued in the $*$-algebra of adjointable operators on a VE-space (Vector Euclidean space) and that are invariant under actions of $*$-semigroups.
Ay, Serdar, Gheondea, Aurelian
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Convolutions, integral transforms and integral equations by means of the theory of reproducing kernels [PDF]
Opuscula Mathematica, 2012 This paper introduces a general concept of convolutions by means of the theory of reproducing kernels which turns out to be useful for several concrete examples and applications.
Luis P. Castro +2 more
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On Weights Which Admit Harmonic Bergman Kernel and Minimal Solutions of Laplace’s Equation
Annales Mathematicae Silesianae, 2022 In this paper we consider spaces of weight square-integrable and harmonic functions L2H(Ω, µ). Weights µ for which there exists reproducing kernel of L2H(Ω, µ) are named ’admissible weights’ and such kernels are named ’harmonic Bergman kernels’. We prove
Żynda Tomasz Łukasz
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On the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions [PDF]
, 2007 We present decompositions of various positive kernels as integrals or sums of positive kernels. Within this framework we study the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions. As a tool, we define a
Alpay, Daniel, Levanony, David
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Extension of Wirtinger's Calculus to Reproducing Kernel Hilbert Spaces and the Complex Kernel LMS [PDF]
, 2010 Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. The primary mathematical tool employed in these methods is the notion of the Reproducing Kernel Hilbert Space.
Bouboulis, Pantelis +1 more
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Reproducing Kernel Hilbert Spaces of Smooth Fractal Interpolation Functions
Fractal and Fractional, 2023 The theory of reproducing kernel Hilbert spaces (RKHSs) has been developed into a powerful tool in mathematics and has lots of applications in many fields, especially in kernel machine learning.
Dah-Chin Luor, Liang-Yu Hsieh
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Thinplate Splines on the Sphere [PDF]
, 2018 In this paper we give explicit closed forms for the semi-reproducing kernels associated with thinplate spline interpolation on the sphere. Polyharmonic or thinplate splines for ${\mathbb R}^d$ were introduced by Duchon and have become a widely used tool ...
Beatson, Rick K., Castell, Wolfgang zu
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