Weighted reproducing Kernel Property on Banach Spaces

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.