Difference between revisions of "Paper:Robert J. Marks II/A generalized Fourier transform and convolution on time scales"
From timescalewiki
| Line 18: | Line 18: | ||
:::Definition 2.3 (2.2): [[Cylinder transformation]] | :::Definition 2.3 (2.2): [[Cylinder transformation]] | ||
:::Definition 2.3 (2.3): [[Inverse cylinder transformation]] | :::Definition 2.3 (2.3): [[Inverse cylinder transformation]] | ||
| + | :::Definition 2.4: [[Hilger pure imaginary]] | ||
:3. The Fourier transform on a time scale | :3. The Fourier transform on a time scale | ||
:4. Convolution on time scales | :4. Convolution on time scales | ||
Revision as of 16:00, 15 January 2023
Robert J. Marks II, Ian 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
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
- 2.1. Relevant time scales
- 3. The Fourier transform on a time scale
- 4. Convolution on time scales
- 5. Classes of time scales arising from convolution
- 6. Examples of discrete convolution on AITS
- 7. Conclusions
