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SUMMARY:The eigenvalue estimation of spatio-spectral limiting operators - 
 Azita Mayeli (City University of New York)
DTSTART:20240716T130000Z
DTEND:20240716T134000Z
UID:TALK218152@talks.cam.ac.uk
DESCRIPTION:Let F\, S be bounded measurable sets in Rd. Let PF : L2 (Rd) &
 rarr\; L2 (Rd) be the orthogonal projection on the subspace of functions w
 ith compact support on F\, and let BS : L2 (Rd) &rarr\; L2 (Rd) be the ort
 hogonal projectionon the subspace of functions with Fourier transforms hav
 ing compact support on S. We define the spatio-spectral limiting operator 
 as a composition of the orthogonal projections BSPF BS : L2 (Rd) &rarr\; L
 2 (Rd).\nThe non-asymptotic eigenvalue distribution of this operator in di
 mension d = 1 has been studied for the case when F and S are both interval
 s. In higher dimensions\, some asymptotic results are known when S and F a
 re balls\, and these results have proved useful for various applications\,
  such as interpolation.\nIn this talk\, I will report on the non-asymptoti
 c distributional estimates of the eigenvalue sequence of this operator for
  d &ge\; 1 for more general spatio and frequency domains F and S\, resepec
 tively. The significance of these estimates lies in their diverse applicat
 ions in wireless communications\, medical imaging\,signal processing\, geo
 physics\, and astronomy.\nThis is a joint work with Kevin Hughes of Edinbu
 rgh Napier University and Arie Israel of The University of Texas at Austin
 .
LOCATION:Seminar Room 1\, Newton Institute
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