Abstract
Series with respect to systems Φ{φn(x)}n=1∞ of measurable and almost everywhere finite functions are discussed. A necessary and sufficient condition for representing any series with respect to a system Φ as a sum of two universal series is formulated. A consequence of the condition is that any series with respect to an arbitrary complete and orthonormal system Φ is a sum of two universal series.
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D. E. Menchoff, Mat. Sb. 20 (2), 197–238 (1947).
S. Kaczmarz and H. Steinhaus, Theorie der Orthogonalreihen (Stechert, New York, 1935; Fizmatlit, Moscow, 1958).
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Original Russian Text © Sh. Tetunashvili, 2017, published in Doklady Akademii Nauk, 2017, Vol. 477, No. 3, pp. 280–281.
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Tetunashvili, S. Functional series representable as a sum of two universal series. Dokl. Math. 96, 578–579 (2017). https://doi.org/10.1134/S106456241706014X
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DOI: https://doi.org/10.1134/S106456241706014X