Zonal function network frames on the sphere

Authors:
H. N. Mhaskar;F. J. Narcowich;J. D. Ward
Affiliations:
Department of Mathematics, California State University, Los Angeles, CA;Department of Mathematics, Texas A&M University, College Station, TX;Department of Mathematics, Texas A&M University, College Station, TX
Venue:
Neural Networks
Year:
2003

Citing 6
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Abstract

We introduce a class of zonal function network frames suitable for analyzing data collected at scattered sites on the surface of the unit sphere of a Euclidean space. Our frames consist of zonal function networks and are well localized. The frames belonging to higher and higher scale wavelet spaces have more and more vanishing polynomial moments. The main technique is applicable in the general setting of separable Hilbert spaces, in which context, we study the construction of new frames by perturbing an orthonormal basis.