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On Hardy kernels as reproducing kernels [PDF]

Canadian Mathematical Bulletin, 2023
Hardy kernels are a useful tool to define integral operators on Hilbertian spaces like L2 (R+) or H2 (C+). These kernels entail an algebraic L1-structure which is used in this work to study the range spaces of those operators as reproducing kernel ...
Jesús Oliva-Maza, Oliva Maza, J.
core   +5 more sources

Duality by reproducing kernels [PDF]

International Journal of Mathematics and Mathematical Sciences, 2003
Let A be a determined or overdetermined elliptic differential operator on a smooth compact manifold X. Write 𝒮A(𝒟) for the space of solutions of the system Au=0 in a domain 𝒟⋐X. Using reproducing kernels related to various Hilbert structures on subspaces
A. Shlapunov, N. Tarkhanov
doaj   +2 more sources

Exploring novel semi-inner product reproducing Kernels in Banach space for robust Kernel methods. [PDF]

PLoS ONE
Kernel methods are widely applied across various domains; however, structural limitations of reproducing kernels in Hilbert spaces pose significant challenges.
Yi Ding, Ying Zhao, Yan Pei
doaj   +2 more sources

On functional reproducing kernels

Open Mathematics, 2023
We show that even if a Hilbert space does not admit a reproducing kernel, there could still be a kernel function that realizes the Riesz representation map.
Zhou Weiqi
doaj   +3 more sources

Nonlinear vertex discriminant analysis with reproducing kernels [PDF]

Statistical Analysis and Data Mining, 2012
Tong Tong Wu, Yichao Wu
exaly   +2 more sources

Commutant lifting and factorization of reproducing kernels

Journal of Functional Analysis, 2005
A general version of the commutant lifting theorem for operators between different spaces is proved. It includes as special cases the lifting theorems of Ball–Trent–Vinnikov and Volberg–Treil.
Serguei Shimorin
exaly   +2 more sources

On Relative Reproducing Kernel Banach Spaces: Definitions, Semi-Inner Product and Feature Maps [PDF]

Sahand Communications in Mathematical Analysis, 2023
In this paper, a special class of relative reproducing kernel Banach spaces a semi-inner product is studied. We extend the concept of relative reproducing kernel Hilbert spaces to Banach spaces. We present these relative reproducing kernel Banach spaces  
Mohammadreza Foroutan
doaj   +1 more source

Some Properties of Reproducing Kernel Banach and Hilbert Spaces [PDF]

Sahand Communications in Mathematical Analysis, 2018
This paper is devoted to the study of reproducing kernel Hilbert spaces. We focus on multipliers of reproducing kernel Banach and Hilbert spaces. In particular, we try to extend this concept and prove some related theorems.
Saeed Hashemi Sababe, Ali Ebadian
doaj   +1 more source

EQUIVALENT CONDITIONS FOR THE EXISTENCE OF UNCONDITIONAL BASES OF REPRODUCING KERNELS IN SPACES OF ENTIRE FUNCTIONS

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
doaj   +1 more source

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
doaj   +1 more source