Abstract

We introduce and study an integral transform whose kernel is Dawson’s integral. The proposed transform is connected to the Fourier sine transform through a classical integral representation of Dawson’s function and to the Glasser transform through an iteration formula. Basic operational properties are developed, including derivative identities, delta-derivative identities, Mellin-transform representations, and an inversion theorem. Several transform pairs are obtained for elementary functions, Gaussian functions, powers multiplied by trigonometric functions, and Bessel functions. The results place the Dawson transform within the broader theory of special-function integral transforms and Parseval–Goldstein-type identities.

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