Integration with respect to a vector measure and function approximation

L. M. García-Raffi, D. Ginestar and E. A. Sánchez-Pérez

Abstract and Applied Analysis, 2000, vol. 5, 1-20

Abstract:

The integration with respect to a vector measure may be applied in order to approximate a function in a Hilbert space by means of a finite orthogonal sequence { f i } attending to two different error criterions. In particular, if Ω ∈ ℝ is a Lebesgue measurable set, f ∈ L 2 ( Ω ) , and { A i } is a finite family of disjoint subsets of Ω , we can obtain a measure μ 0 and an approximation f 0 satisfying the following conditions: (1) f 0 is the projection of the function f in the subspace generated by { f i } in the Hilbert space f ∈ L 2 ( Ω , μ 0 ) . (2) The integral distance between f and f 0 on the sets { A i } is small.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:648976

DOI: 10.1155/S1085337501000227

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