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Prolate spheroidal wave functions on a disc—Integration and approximation of two-dimensional bandlimited functions

Authors
Journal
Applied and Computational Harmonic Analysis
1063-5203
Publisher
Elsevier
Publication Date
Volume
22
Issue
2
Identifiers
DOI: 10.1016/j.acha.2006.07.002
Keywords
  • Bandlimited
  • Quadrature
  • Approximation
  • Interpolation
  • Prolate Spheroidal Wave Functions

Abstract

Abstract We consider the problem of integrating and approximating 2D bandlimited functions restricted to a disc by using 2D prolate spheroidal wave functions (PSWFs). We derive a numerical scheme for the evaluation of the 2D PSWFs on a disc, which is the basis for the numerical implementation of the presented quadrature and approximation schemes. Next, we derive a quadrature formula for bandlimited functions restricted to a disc and give a bound on the integration error. We apply this quadrature to derive an approximation scheme for such functions. We prove a bound on the approximation error and present numerical results that demonstrate the effectiveness of the quadrature and approximation schemes.

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