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Reproducing Kernel Hilbert Space vs. Frame Estimates
Mathematics, 2015 We consider conditions on a given system F of vectors in Hilbert space H, forming a frame, which turn H into a reproducing kernel Hilbert space. It is assumed that the vectors in F are functions on some set Ω .
Palle E. T. Jorgensen, Myung-Sin Song
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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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INFERENCE ON THE REPRODUCING KERNEL HILBERT SPACES
Universal Journal of Mathematics and Mathematical Sciences, 2021 Summary: Learning and interpolation are two extreme variants of the same problem, the object of which is to construct a function which is supposed to reasonably approximate an unknown function of which only a certain number of samples are known.
Agbokou, Komi, Mensah, Yaogan
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Integration in reproducing kernel Hilbert spaces of Gaussian kernels [PDF]
Mathematics of Computation, 2021 The Gaussian kernel plays a central role in machine learning, uncertainty quantification and scattered data approximation, but has received relatively little attention from a numerical analysis standpoint. The basic problem of finding an algorithm for efficient numerical integration of functions reproduced by Gaussian kernels has ...
Toni Karvonen +2 more
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Reproducing kernel method for solving wiener-hopf equations of the second kind [PDF]
Journal of Hyperstructures, 2016 This paper proposed a reproducing kernel method for solving Wiener-Hopf equations of the second kind. In order to eliminate the singularity of the equation, a transform is used.
Azizallah Alvandi +2 more
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A Primer on Reproducing Kernel Hilbert Spaces [PDF]
Foundations and Trends® in Signal Processing, 2015 Reproducing kernel Hilbert spaces are elucidated without assuming prior familiarity with Hilbert spaces. Compared with extant pedagogic material,greater care is placed on motivating the definition of reproducing kernel Hilbert spaces and explaining when and why these spaces are efficacious.
Jonathan H. Manton +1 more
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Metamorphosis of images in reproducing kernel Hilbert spaces [PDF]
Advances in Computational Mathematics, 2015 Metamorphosis is a method for diffeomorphic matching of shapes, with many potential applications for anatomical shape comparison in medical imagery, a problem which is central to the field of computational anatomy. An important tool for the practical application of metamorphosis is a numerical method based on shooting from the initial momentum, as this
Casey L. Richardson, Laurent Younes
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ON THE INCLUSION RELATION OF REPRODUCING KERNEL HILBERT SPACES [PDF]
Analysis and Applications, 2013 To help understand various reproducing kernels used in applied sciences, we investigate the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of feature maps of the corresponding reproducing kernels are established.
Haizhang Zhang, Liang Zhao
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Проблемы анализа, 2021 We consider a reproducing kernel radial Hilbert space of entire functions and prove the equivalence of several sufficient conditions for the existence of unconditional bases of reproducing kernels in such spaces.
K. P. Isaev, R. S. Yulmukhametov
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Mathematical Modelling and Analysis, 2021 The main aim of this paper is to present a hybrid scheme of both meshless Galerkin and reproducing kernel Hilbert space methods. The Galerkin meshless method is a powerful tool for solving a large class of multi-dimension problems.
Mehdi Mesrizadeh, Kamal Shanazari
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