Relative reproducing kernels in vector-valued Hilbert and Banach spaces

TL;DR

This paper explores the extension of reproducing kernels to relative reproducing kernels within vector-valued Hilbert spaces, providing new theoretical insights into their properties and applications.

Contribution

It introduces the concept of relative reproducing kernels in vector-valued Hilbert spaces and proves foundational theorems about their structure and behavior.

Findings

Extension of reproducing kernels to relative kernels

Theoretical theorems on properties of relative kernels

Framework for future applications in vector-valued spaces

Abstract

This paper is devoted to the study of vector valued reproducing kernel Hilbert spaces. We focus on reproducing kernels in vector-valued reproducing kernel Hilbert spaces. In particular we extend reproducing kernels to relative reproducing kernels and prove some theorems in this subject.