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In 1961, Bargmann introduced the classical Segal–Bargmann transform and in 1984, Cholewinsky introduced the generalized Segal–Bargmann transform. These two transforms are the aim of many works, and have many applications in mathematics. In this paper, we introduce the Weinstein-type Segal–Bargmann transform; and we prove for this transform Plancherel and inversion formulas. Next, we give a relation between the transformand the Weinstein transformin. As applications, we establish a local-type uncertainty inequalities (two versions) and a dispersion inequality for.

Inversion formula and uncertainty inequalities for the Weinstein-type Segal–Bargmann transform