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- W2952668473 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 (mu). That is, we consider recursive and orthogonal decompositions for the Hilbert space L^2(mu) where mu 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." @default.
- W2952668473 created "2019-06-27" @default.
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- W2952668473 date "2005-12-30" @default.
- W2952668473 modified "2023-09-27" @default.
- W2952668473 title "Localized bases in L^2(0,1) and their use in the analysis of Brownian motion" @default.
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