Orthogonal systems in $L^2$ spaces of a vector measure | Zendy

Eduardo Fernández | Zendy

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Orthogonal systems in $L^2$ spaces of a vector measure

Author(s) -

Eduardo Fernández

Publication year - 2013

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1208-23

Subject(s) - mathematics , measure (data warehouse) , infinite dimensional vector function , scalar (mathematics) , banach space , pure mathematics , vector space , space (punctuation) , vector valued function , orthogonal polynomials , discrete mathematics , lp space , banach manifold , computer science , geometry , database , operating system

Let m:S \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 L2(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.

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