Turkish Journal of Mathematics
DOI
10.3906/mat-1208-23
Abstract
Let m:\Sigma \to X be a Banach space valued countably additive vector measure. In this paper we present a procedure to construct an m-orthogonal system in the space L^2(m) of square integrable functions with respect to m. If the vector measure is constructed from a family of indeterminate scalar measures, it is possible to obtain a family of polynomials that is orthogonal with respect to this vector measure. On the other hand, if the vector measure is fixed, then we can obtain sequences of orthogonal functions using the Kadec-Pelczynski disjointification method.
Keywords
Orthogonal sequences, vector measures, integration
First Page
981
Last Page
992
Recommended Citation
FERNÁNDEZ, EDUARDO JIMÉNEZ
(2013)
"Orthogonal systems in L^2 spaces of a vector measure,"
Turkish Journal of Mathematics: Vol. 37:
No.
6, Article 9.
https://doi.org/10.3906/mat-1208-23
Available at:
https://journals.tubitak.gov.tr/math/vol37/iss6/9
