Abstract

The paper is devoted to the study of 2D version special functions generalizing the famous Slepian functions. As a consequence, many desirable spectral properties of the corresponding weighted finite Fourier transform are deduced from the rich literature. In particular, a similar aspect related to Slepian's seminal papers is the investigation of differential operators that commute with appropriate integral operators. Finally, we provide some analytic expressions for the finite Fourier transforms of the disk polynomials and the two variables Gegenbauer polynomials.

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