Preprint Article Version 1 This version is not peer-reviewed

Weighted Reproducing Kernel Property on Banach Spaces

Version 1 : Received: 25 March 2019 / Approved: 28 March 2019 / Online: 28 March 2019 (11:24:47 CET)

How to cite: Hashemi Sababe, S. Weighted Reproducing Kernel Property on Banach Spaces. Preprints 2019, 2019030263 (doi: 10.20944/preprints201903.0263.v1). Hashemi Sababe, S. Weighted Reproducing Kernel Property on Banach Spaces. Preprints 2019, 2019030263 (doi: 10.20944/preprints201903.0263.v1).

Abstract

In this paper, we study the weighted reproducing kernels. We introduce a generalization of weighted reproducing property and extend it to relative reproducing property on Banach spaces. This generalization will develop the parallel computing and it can be used as a base of parallel learning for machines especially in the case that there are non-homogenous weighted hypothesis. This methods formulate learning and estimation problems in a relative reproducing kernel Banach space (RRKBS) of functions defined on the data domain, expanded in terms of a kernel.

Subject Areas

Reproducing property, learning theory, representer theorems.

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