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In this article, we introduce a novel numerical scheme, the iterative reproducing kernel method (IRKM), for providing numerical approximate solutions of a certain class of time-fractional boundary value problem within favorable aspects of the reproducing
Mohammed Al-Smadi
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Approximation properties for multiplier algebras of reproducing kernel Hilbert spaces [PDF]
In this note, it is proved that multiplier algebras of analytic reproducing kernel Hilbert spaces which are compatible with the action of the torus group possess Kraus’ completely contractive approximation property (CCAP) and, consequently, have the ...
Barbian, Christoph, Barbian Christoph
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Learnability in Hilbert Spaces with Reproducing Kernels
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Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces
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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Density Problem and Approximation Error in Learning Theory
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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The central problem of this study is to represent any holomorphic and square integrable function on the Kepler manifold in the series form based on Fourier analysis.
Zeyuan Song, Zuoren Sun
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Reproducing kernel Hilbert spaces and variable metric algorithms in PDE constrained shape optimisation [PDF]
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape optimisation ...
M. Eigel +3 more
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Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations
On the basis of reproducing kernel Hilbert spaces theory, an iterative algorithm for solving some nonlinear differential-difference equations (NDDEs) is presented.
Reza Mokhtari +2 more
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GPU-Accelerated Partially Linear Multiuser Detection for 5G and Beyond URLLC Systems
We have implemented a recently proposed partially linear multiuser detection algorithm in reproducing kernel Hilbert spaces (RKHSs) on a GPU-accelerated platform.
Matthias Mehlhose +8 more
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Operators associated with soft and hard spectral edges from unitary ensembles. [PDF]
Using Hankel operators and shift-invariant subspaces on Hilbert space, this paper develops the theory of integrable operators associated with soft and hard edges of eigenvalues distributions of random matrices. Such Tracy--Widom operators are realized as
Blower, Gordon
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