Abstract
It can be extended to \(\mathbb {R}\) by the periodicity of period 1. Each Haar function is continuous from the right and the Haar system H is orthonormal on [0, 1).
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References
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Farkov, Y.A., Manchanda, P., Siddiqi, A.H. (2019). Haar–Vilenkin Wavelet. In: Construction of Wavelets Through Walsh Functions. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-13-6370-2_6
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DOI: https://doi.org/10.1007/978-981-13-6370-2_6
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