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arXiv · 0808.1173

Frame and wavelet systems on the sphere

Margit Pap
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Abstract

In this paper we formulate a weighted version of minimum problem (1.4) on the sphere and we show that, for $K\le L$, if $\set{\phi_k}^K_{k=1}$ consists of the spherical functions with degree less than $N$ we can localize the points $(\xi_1,...,\xi_L)$ on the sphere so that the solution of this problem is the simplest possible. This localization is connected to the discrete orthogonality of the spherical functions which was proved in [3]. Using these points we construct a frame system and a wavelet system on the sphere and we study the properties of these systems. For $K>L$ a similar construction was made in paper [4], but in that case the solution of the minimum problem (1.4) is not as efficient as it is in our case. The analogue of Fej\'er and de la Val\'ee-Poussin summation methods introduced in [3] can be expressed by the frame system introduced in this paper.

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Margit Pap. 2008-08-08. Frame and wavelet systems on the sphere. https://arxiv.org/abs/0808.1173

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