Functional series representable as a sum of two universal series

Аннотация

Series with respect to systems Φ{φ_n(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.