Hankel matrix transforms and operators

Hankel operators and Hankel transforms are required in a number of applications. This article proves a number of theorems that efficiently and accurately approximates a function using Hankel transforms and Hankel sum. A characterization of the Hankel matrix sequences and Hankel matrix of semi-periodic and almost periodic sequences are also given. This article also introduces the concepts of almost periodic Hankel matrix, multiplicative Hankel matrix and normal almost periodic Hankel matrix. Applications to trigonometric sequences are given.