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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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New reproducing kernel functions in the reproducing kernel Sobolev spaces
AIMS Mathematics, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Akgul, Ali +2 more
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Radial kernels and their reproducing kernel Hilbert spaces
Journal of Complexity, 2010 Let \(R\) be a continuous convex function on a Hilbert space \(H\). In learning theory, \[ A(\lambda):= \inf_{h\in H} \{\lambda\| h\|^2+ R(h)\}- \inf_{h\in H} R(h) \] is called an approximation error function. Here, \(H\) is a reproducing kernel Hilbert space (RKHS) of functions on \(\mathbb{R}^d\), i.e., such that the evaluations \(\delta_x: h\mapsto ...
Clint Scovel +3 more
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Functionals with extrema at reproducing kernels [PDF]
, 2022 We show that certain monotone functionals on the Hardy spaces and convex functionals on the Bergman spaces are maximized at the normalized reproducing kernels among the functions of norm 1, thus proving the contractivity conjecture of Pavlović and of ...
Kulikov, Aleksei
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Reproducing Kernels of Weight Square-Summable Sequences Hilbert Spaces
Annales Mathematicae Silesianae, 2019 In this paper we will introduce the concept of weighted reproducing kernel of l2(ℂ) space, in similiar way as it is done in case of weighted reproducing kernel of Bergman space.
Żynda Tomasz Łukasz
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Reproducing Kernels for q-Jacobi Polynomials [PDF]
Proceedings of the American Mathematical Society, 1977 We derive a family of reproducing kernels for the q -Jacobi polynomials Φ
Al-Salam, Waleed A. +1 more
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Density Problem and Approximation Error in Learning Theory
Abstract and Applied Analysis, 2013 We study the density problem and approximation error of reproducing kernel Hilbert spaces for the purpose of learning theory. For a Mercer kernel on a compact metric space (, ), a characterization for the generated reproducing kernel Hilbert space (RKHS)
Ding-Xuan Zhou
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Conditional mean embedding and optimal feature selection via positive definite kernels [PDF]
Opuscula Mathematica, 2023 Motivated by applications, we consider new operator-theoretic approaches to conditional mean embedding (CME). Our present results combine a spectral analysis-based optimization scheme with the use of kernels, stochastic processes, and constructive ...
Palle E.T. Jorgensen +2 more
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Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces
, 2011 The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. In particular, when the involved kernel is analytic in the sampling parameter it can be stated in an abstract setting of reproducing kernel Hilbert spaces
Hernández-Medina, Miguel A. +7 more
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Detecting periodicities with Gaussian processes [PDF]
PeerJ Computer Science, 2016 We consider the problem of detecting and quantifying the periodic component of a function given noise-corrupted observations of a limited number of input/output tuples.
Nicolas Durrande +3 more
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