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Abstract  

Upper and lower error bounds for an optimal 2-point quadrature rule of open type are derived. These error bounds are sharp. Applications in numerical integration are given

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References [1] Bojanov , B. D. 1982 Oscillating polynomials of least L 1 -norm Hammerlin , G. (eds.) Numerical Integration

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Being interested in (rotation-)invariant pseudodifferential equations of satellite problems corresponding to spherical orbits, we are reasonably led to generating kernels that depend only on the spherical distance, i.\,e., in the language of modern constructive approximation form spherical radial basis functions. In this paper approximate identities generated by such (rotation-invariant) kernels which are additionally locally supported are investigated in detail from theoretical as well as numerical point of view. So-called spherical difference wavelets are introduced. The wavelet transforms are evaluated by the use of a numerical integration rule, that is based on Weyl's law of equidistribution. This approximate formula is constructed such that it can cope with millions of (satellite) data. The approximation error is estimated on the orbital sphere. Finally, we apply the developed theory to the problems of satellite-to-satellite tracking (SST) and satellite gravity gradiometry (SGG).

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] Dragomir , S. S. and Rassias , T. M. , Ostrowski Type Inequalities and Applications in Numerical Integration , Springer Netherlands, 2002 . [7

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.1007/BF01203463 . [11] Lubinsky , D. S. , Sidi , A. 2007 Biorthogonal polynomials and numerical integration formulas for infinite ntervals J. Num. Analysis, Industrial and Appl. Math. 2 1

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