Functional series representable as a sum of two universal series

Doklady Mathematics - Tập 96 - Trang 578-579 - 2018
Sh. Tetunashvili1,2
1Razmadze Mathematical Institute, Tbilisi State University, Tbilisi, Georgia
2Georgian Technical University, Tbilisi, Georgia

Tóm tắt

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.

Tài liệu tham khảo

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).