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Orthonormal expansions and the principle of uniform boundedness
Published online by Cambridge University Press: 17 April 2009
Abstract
Let {φν: ν ∈ N (non-negative integers)} ⊆ C[0, 1] be a complete orthonormal sequence of complex-valued functions in L2[0, 1], {λν: ν ∈ N} and {λνμ: ν, μ ∈ N} be sequences of complex numbers. In this paper, the necessary and sufficient conditions are developed for the series to converge and also to exist, in C[0, 1] for each f ∈ L1[0, 1] where .
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- Copyright © Australian Mathematical Society 1991