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, issue 4, 207-226

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 {fi} attending to two different error criterions. In particular, if Ω ∈ ℝ is a Lebesgue measurable set, f ∈ L2(Ω), and {Ai} is a finite family of disjoint subsets of Ω, we can obtain a measure μ0 and an approximation f0 satisfying the following conditions: (1) f0 is the projection of the function f in the subspace generated by {fi} in the Hilbert space f ∈ L2(Ω, μ0). (2) The integral distance between f and f0 on the sets {Ai} is small.

Date: 2000
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https://doi.org/10.1155/S1085337501000227

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:5:y:2000:i:4:p:207-226

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