Mathematical proof shows Haar series coefficients recoverability via finite function integrability.
The existence is proved of a sequence of natural numbers of zero density with the following property: If the subsequence of partial sums of a Haar series with indices from this sequence converges everywhere to an everywhere finite function integrable in the sense of Perron, then the given series is the Fourier–Haar series of its sum.
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Gevorkyan et al. (2026) studied this question.
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