# Slepian functions on the sphere, generalized Gaussian quadrature rule

@article{Miranian2004SlepianFO, title={Slepian functions on the sphere, generalized Gaussian quadrature rule}, author={L Miranian}, journal={Inverse Problems}, year={2004}, volume={20}, pages={877 - 892} }

Denote by K the operator of ‘time–band–time’ limiting on the surface of the sphere and consider the problem of computing singular vectors of K. This problem can be reduced to a simpler task of computing eigenfunctions of a differential operator, if a differential operator, which commutes with K and has a simple spectrum, can be exhibited. In Grünbaum et al (1982 SIAM J. Appl. Math. 42 941–55) such a second-order differential operator commuting with K on the appropriate subspaces was constructed…

## 12 Citations

Vectorial Slepian Functions on the Ball

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Abstract Due to the uncertainty principle, a function cannot be simultaneously limited in space as well as in frequency. The idea of Slepian functions, in general, is to find functions that are at…

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We pose and solve the analogue of Slepian’s time–frequency concentration problem in the two-dimensional plane, for applications in the natural sciences. We determine an orthogonal family of strictly…

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Two related approximation problems are formulated and solved in Hardy spaces of the disc and annulus. With practical applications in mind, truncated versions of these problems are analysed, where the…

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A quadratic variational framework for solving a broad class of signal design problems on the 2-sphere is introduced and a joint 3-D beamforming application is formulated which achieves optimal directivity and spatial resolution simultaneously.

Sparse regularization of a joint inversion of gravitational data and normal mode anomalies

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To recover the density of the Earth we invert Newton's gravitational potential. It is a well-known fact that this problem is ill-posed. Thus, we need to develop a regularization method to solve it…