Strobl22

Applied Harmonic Analysis and Friends

June 19th - 25th 2022

Strobl, AUSTRIA

"Properties of Clifford Prolate Spheroidal Wave Functions"

Baghal Ghaffari, Hamed

In this talk, we introduce important properties of Clifford Prolate Spheroidal Wave Functions (CPSWFs). We first review the Clifford Legendre polynomials, and the Clifford Prolate differential equation whose eigenfunctions constitute what we call as CPSWFs. We show that the radial part of CPSWFs satisfies the Sturm–Liouville theory which allows us to talk about relevant properties including the zeros of CPSWFs. We present that CPSWFs are also the eigenfunctions of an appropriate time-frequency limiting operator. We mention that the eigenvalues of the latter operator has a non-degeneracy property, among others. Finally, we highlight some spectral concentration and spectrum accumulation properties of the CPSWFs.

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