Journal article
Localized bases in L2 (0, 1) and their use in the analysis of Brownian motion
Journal of Approximation Theory, Vol.151(1), pp.20-41
2008
DOI: 10.1016/j.jat.2007.08.002
Abstract
Motivated by problems on Brownian motion, we introduce a recursive scheme for a basis construction in the Hilbert space L 2 ( 0 , 1 ) which is analogous to that of Haar and Walsh. More generally, we find a new decomposition theory for the Hilbert space of square-integrable functions on the unit-interval, both with respect to Lebesgue measure, and also with respect to a wider class of self-similar measures μ . That is, we consider recursive and orthogonal decompositions for the Hilbert space L 2 ( μ ) where μ is some self-similar measure on [ 0 , 1 ] . Up to two specific reflection symmetries, our scheme produces infinite families of orthonormal bases in L 2 ( 0 , 1 ) . Our approach is as versatile as the more traditional spline constructions. But while singly generated spline bases typically do not produce orthonormal bases, each of our present algorithms does.
Details
- Title: Subtitle
- Localized bases in L2 (0, 1) and their use in the analysis of Brownian motion
- Creators
- Palle E.T JorgensenAnilesh Mohari
- Resource Type
- Journal article
- Publication Details
- Journal of Approximation Theory, Vol.151(1), pp.20-41
- DOI
- 10.1016/j.jat.2007.08.002
- ISSN
- 0021-9045
- eISSN
- 1096-0430
- Language
- English
- Date published
- 2008
- Academic Unit
- Mathematics
- Record Identifier
- 9983985823402771
Metrics
80 Record Views