Hilbert Matrix and Difference Operator of Order m
Murat Kiri\c{s}ci, Harun Polat
TL;DR
This paper explores the applications of Hilbert matrices in image processing and cryptology, introduces new matrix domains, investigates their properties, and characterizes related transformations.
Contribution
It presents novel matrix domains based on Hilbert matrices, analyzes their properties, and provides a framework for transformations in these spaces.
Findings
New matrix domains constructed and analyzed
Properties and dual spaces of these domains characterized
Examples of transformations in the new spaces provided
Abstract
In this paper, firstly, some applications of Hilbert matrix in image processing and cryptology are mentioned and an algorithm related to the Hilbert view of a digital image is given. In section 2, the new matrix domains are constructed and some properties are investigated. Furthermore, dual spaces of new matrix domains are computed and matrix transformations are characterized. In last section, examples of transformations of new spaces are given.
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