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math.FA2026
A Modern Functional Analytic Tour of the Fourier-Bessel Transform
Cameron L. Williams
In this paper, we review the theory of the Fourier--Bessel transform. The Fourier--Bessel transform is an integral transform on the half-line that generalizes the Fourier cosine tr…
math.FA2021
Segal-Bargmann Transforms Associated to a Family of Coupled Supersymmetries
Cameron L. Williams
The Segal-Bargmann transform is a Lie algebra and Hilbert space isomorphism between real and complex representations of the oscillator algebra. The Segal-Bargmann transform is usef…
math.FA2014★ 7 cited
Fourier and Beyond: Invariance Properties of a Family of Integral Transforms
Cameron L. Williams, Bernhard G. Bodmann, Donald J. Kouri
The Fourier transform is typically seen as closely related to the additive group of real numbers, its characters and its Haar measure. In this paper, we propose an alternative view…