Schauder-type expansions of continuous functions on the unit interval |
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Authors: | Henry C. Finlayson |
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Affiliation: | Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2 |
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Abstract: | Let the space of continuous functions on [0, 1] which vanish at 0 be denoted by C. It will be shown that for any complete orthonormal set of functions {αi(s)} of bounded variation and such that αi(1) = 0, there is a simply described linear combination of the continuous functions {∝0tαi(s) ds} which converges uniformly to x(t) for almost all x ε C (“almost all” in the sense of Wiener measure). |
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