Difference between revisions of "Paper:Robert J. Marks II/A generalized Fourier transform and convolution on time scales"
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:2. Background | :2. Background | ||
::2.1. Relevant time scales | ::2.1. Relevant time scales | ||
| − | :::[[Real numbers]] | + | :::Section 2.1(a): [[Real numbers]] |
| − | :::[[Multiples of integers]] | + | :::Section 2.1(b): [[Multiples of integers]] |
::2.2 The Hilger complex plane | ::2.2 The Hilger complex plane | ||
| − | :::[[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 | :3. The Fourier transform on a time scale | ||
| + | ::[[Marks-Gravagne-Davis Fourier transform]] | ||
:4. Convolution on time scales | :4. Convolution on time scales | ||
:5. Classes of time scales arising from convolution | :5. Classes of time scales arising from convolution | ||
Latest revision as of 16:01, 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
