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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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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Generalized Mercer Kernels and Reproducing Kernel Banach Spaces [PDF]
Memoirs of the American Mathematical
Society, 2019 128 pages and 4 ...
Xu, Yuesheng, Ye, Qi
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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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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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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 ...
Kumari, Rani +3 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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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 n ( α , β ) ( x ) = 2 Φ 1 (
Al-Salam, Waleed A. +1 more
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