Open Access
2000 Integration with respect to a vector measure and function approximation
L. M. García-Raffi, D. Ginestar, E. A. Sánchez-Pérez
Abstr. Appl. Anal. 5(4): 207-226 (2000). DOI: 10.1155/S1085337500000221


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.


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L. M. García-Raffi. D. Ginestar. E. A. Sánchez-Pérez. "Integration with respect to a vector measure and function approximation." Abstr. Appl. Anal. 5 (4) 207 - 226, 2000.


Published: 2000
First available in Project Euclid: 10 April 2003

zbMATH: 1014.46012
MathSciNet: MR1885467
Digital Object Identifier: 10.1155/S1085337500000221

Primary: 46A32

Rights: Copyright © 2000 Hindawi

Vol.5 • No. 4 • 2000
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