Paper:Robert J. Marks II/A generalized Fourier transform and convolution on time scales

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Robert J. Marks IIIan A. Gravagne and John M. Davis: A generalized Fourier transform and convolution on time scales

Published $2008$, Journal of Mathematical Analysis and Applications.


Online copies

[1]

Contents

1. Introduction
2. Background
2.1. Relevant time scales
Section 2.1(a): Real numbers
Section 2.1(b): Multiples of integers
2.2 The Hilger complex plane
Definition 2.2: Hilger complex plane
Definition 2.2: Hilger real axis
Definition 2.2: Hilger alternating axis
Definition 2.2: Hilger circle
Definition 2.3: Cylinder strip
Definition 2.3 (2.2): Cylinder transformation
Definition 2.3 (2.3): Inverse cylinder transformation
Definition 2.4: Hilger pure imaginary
3. The Fourier transform on a time scale
Marks-Gravagne-Davis Fourier transform
4. Convolution on time scales
5. Classes of time scales arising from convolution
6. Examples of discrete convolution on AITS
7. Conclusions