Optimally localized approximate identities on the 2-sphere. (English) Zbl 1229.41023
The author introduces a method to construct approximate identities on the 2-sphere that have an optimal localization. By using such an approach the author accelerates the calculations of approximations on the 2-sphere with a comparably small increase of the error. The localization measure in the optimization problem includes a weight function that is chosen under some constraints. The optimally localizing identity for a certain weight function is calculated and numerically tested.
Reviewer: Vijay Gupta (New Delhi)
MSC:
| 41A35 | Approximation by operators (in particular, by integral operators) |
| 41A55 | Approximate quadratures |
| 42C25 | Uniqueness and localization for orthogonal series |
| 65D15 | Algorithms for approximation of functions |
Keywords:
approximate identity; convergence; convolution; existence; fast approximation; sphere; uniquenessReferences:
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