Integration with respect to a vector measure and function
approximation

Dublin Core

Title

Integration with respect to a vector measure and function
approximation

Description

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.

Creator

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

Publisher

Abstract and Applied Analysis

Date

2000

Rights

Copyright © 2000 Hindawi Publishing Corporation.

Language

en

Identifier

https://doi.org/10.1155/S1085337501000227

Citation

L. M. García-Raffi, D. Ginestar, and E. A. Sánchez-Pérez, “Integration with respect to a vector measure and function
approximation,” Open Access Journal Archives, accessed January 19, 2022, https://oajour.info/items/show/365.