Abstract and Applied Analysis

Abstract and Applied Analysis / 2000 / Article

Open Access

Volume 5 |Article ID 648976 | https://doi.org/10.1155/S1085337501000227

L. M. García-Raffi, D. Ginestar, E. A. Sánchez-Pérez, "Integration with respect to a vector measure and function approximation", Abstract and Applied Analysis, vol. 5, Article ID 648976, 20 pages, 2000. https://doi.org/10.1155/S1085337501000227

Integration with respect to a vector measure and function approximation

Received13 May 2000

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 is a Lebesgue measurable set, fL2(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 fL2(Ω,μ0). (2) The integral distance between f and f0 on the sets {Ai} is small.

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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