Highly localized kernels on space of homogeneous type

TL;DR

This paper explores the concept of highly localized kernels on spaces of homogeneous type, clarifying their properties and providing a framework for their application across various localizable spaces.

Contribution

It introduces a unified approach to understanding localized kernels on homogeneous spaces and clarifies the concept of localness within this context.

Findings

Provides a list of localizable spaces of homogeneous type

Clarifies the concept of localness for kernels

Establishes a framework for applying localized kernels

Abstract

Highly localized kernels based on orthogonal polynomials have been studied and utilized over several regular domains. Much of the results deduced via these kernels can be treated uniformly in the framework of localizable spaces of homogeneous type. We clarify the concept of localness and provide a list of such localizable spaces.