Difference between revisions of "Cuchta-Georgiev Fourier transform"
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| + | Let $\mathbb{T}$ be a [[time scale]] and let $s \in \mathbb{T}$. Let $f \colon \mathbb{T} \rightarrow \mathbb{C}$ be a function. Define the Cuchta-Georgiev Fourier transform of $f$ centered at $s$ by | ||
| + | $$\mathcal{F}_{\mathbb{T}}\{f\}(z;s)=\displaystyle\int_{\mathbb{T}} f(\tau)e_{\ominus iz}(\sigma(t),\tau) \Delta \tau,$$ | ||
| + | where $\ominus$ denotes the [[circle minus]] operation and $e_{\ominus iz}$ denotes the [[delta exponential]]. | ||
=See also= | =See also= | ||
[[Marks-Gravagne-Davis Fourier transform]] | [[Marks-Gravagne-Davis Fourier transform]] | ||
Revision as of 16:22, 15 January 2023
Let $\mathbb{T}$ be a time scale and let $s \in \mathbb{T}$. Let $f \colon \mathbb{T} \rightarrow \mathbb{C}$ be a function. Define the Cuchta-Georgiev Fourier transform of $f$ centered at $s$ by $$\mathcal{F}_{\mathbb{T}}\{f\}(z;s)=\displaystyle\int_{\mathbb{T}} f(\tau)e_{\ominus iz}(\sigma(t),\tau) \Delta \tau,$$ where $\ominus$ denotes the circle minus operation and $e_{\ominus iz}$ denotes the delta exponential.
