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http://repositorio.yachaytech.edu.ec/handle/123456789/521| Title: | 2-Dimensional Quaternionic Fourier Transform and Applications |
| Authors: | Ariza, Eusebio Chipantiza Punina, Carlos Javier |
| Keywords: | Cuaternión Transformada de Fourier Cuaterniónica Bidi- mensional (izquierda) Ecuación de calor Quaternion Two-dimensional (left) Quaternion Fourier Trans- form Heat equation. |
| Issue Date: | Jul-2022 |
| Publisher: | Universidad de Investigación de Tecnología Experimental Yachay |
| Abstract: | En este trabajo, definimos la Transformada de Fourier Cuaterniónica Bidi-mensional (izquierda) (2D-QFT) de f ∈ L1 (R2; H), la cual es la función Fq{ f } : R2 → H definida por Fq{ f }(ω) = ̂ f (ω) = ∫R2 e−μω·x f (x)d2x, donde x = x1e1 + x2e2, ω = ω1e1 + ω2e2, con kernel de Fourier cu-aterniónico e−μω·x tal que |μ| = 1. Derivamos las propiedades de desplazamiento, modulación y convolución y establecemos el teorema de Plancherel y el teorema de derivación vecto-rial. Además, estudiaremos la aplicación de esta transformada de Fourier a la resolución de la ecuación del calor. |
| Description: | In this work, we define the Two-dimensional (left) Quaternion Fourier Transform (2D-QFT) of f ∈ L1 (R2; H), which is the function Fq{ f } : R2 → H defined by Fq{ f }(ω) = ̂ f (ω) =∫R2 e−μω·x f (x)d2x, where x = x1e1 + x2e2, ω = ω1e1 + ω2e2, with quaternion Fourier kernel e−μω·x such that |μ| = 1. We derive the shift, modulation, and convolution properties and estab-lish the Plancherel and vector differential theorem. Furthermore, we will study the application of this Fourier transform to the resolution to the heat equation. |
| URI: | http://repositorio.yachaytech.edu.ec/handle/123456789/521 |
| Appears in Collections: | Matemática |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| ECMC0098.pdf | 1.08 MB | Adobe PDF | View/Open |
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