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Some further estimates of the prolate spheroidal wave functions and their spectrum
-
Aline Bonami
and
Abderrazek Karoui
Published/Copyright:
March 31, 2015
Abstract
We complete here our recent work on explicit approximations of the Prolate Spheroidal Wave Functions (PSWFs) on the interval [-1,+1] and their associated spectra by pushing forward the methods in view of new results. We give in particular approximations of the ratio between large and small oscillations of PSWFs as well of the transition bandwidth for which the PSWF stops to take its largest values at the boundary of the interval. The aim of this work is two folds. On one hand, we prove a bunch of properties of the PSWFs and on the other hand, we illustrate the theoretical results by some numerical experiments.
Keywords: Prolate spheroidal wave
functions; asymptotic and uniform estimates; eigenvalues and eigenfunctions; Sturm–Liouville operator; sinc kernel operator
Funding source: Tunisian DGRST
Award Identifier / Grant number: UR 13 ZS 47
Received: 2014-11-15
Revised: 2015-2-5
Accepted: 2015-2-7
Published Online: 2015-3-31
Published in Print: 2015-4-1
© 2015 by De Gruyter
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- Frontmatter
- Geometric and harmonic analysis on homogeneous spaces and applications: Hammamet, December 2013
- On discontinuous groups acting on (ℍ2n+1r × ℍ2n+1r)/Δ
- Some further estimates of the prolate spheroidal wave functions and their spectrum
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Articles in the same Issue
- Frontmatter
- Geometric and harmonic analysis on homogeneous spaces and applications: Hammamet, December 2013
- On discontinuous groups acting on (ℍ2n+1r × ℍ2n+1r)/Δ
- Some further estimates of the prolate spheroidal wave functions and their spectrum
- On the connectedness of the Chabauty space of a locally compact prosolvable group
- Holomorphically induced representations of exponential solvable semi-direct product groups ℝ ⋉ ℝn
- The positivity of the transmutation operators associated with the Cherednik operators attached to the root system of type A2
