WEIGHTED REPRODUCING KERNEL PROPERTY ON BANACH SPACES

Year 2025, Volume: 15 Issue: 12, 2809 - 2827, 06.12.2025

Saeed Hashemi Sababe , Nader Biranvand

Abstract

Weighted Reproducing Kernel Banach Spaces (WRKBS) extend kernel theory by incorporating weights to enhance modeling flexibility. This paper defines WRKBS, explores their theoretical foundations, and demonstrates their effectiveness in regression, classification, and clustering. Numerical experiments validate their advantages in structured data modeling and symmetry-aware learning. Applications span computer vision, physics-based modeling, and graph-based learning, with future directions in scalable algorithms and deep learning integration.

Keywords

Reproducing Kernels , Banach Spaces , Gaussian Process

Ethical Statement

The authors declare that the work presented in this manuscript is original and has not been published previously. All authors have read and approved the final version of the manuscript and have agreed to its submission to this journal. There are no conflicts of interest, financial or otherwise, associated with this work. Any sources of funding or support have been appropriately acknowledged within the manuscript.

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