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 regulated. 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.

Properties

Cuchta-Georgiev Fourier transform of delta derivatives

See also

Marks-Gravagne-Davis Fourier transform

References