On the square and the spherical partial sums of multiple orthogonal series

1981 ◽  
Vol 37 (1-3) ◽  
pp. 255-261
Author(s):  
F. Móricz
Keyword(s):  
Orthogonal Series ◽  
Partial Sums ◽  
Multiple Orthogonal Series

On the order of partial sums of general orthogonal series

1969 ◽  
Vol 6 (4) ◽  
pp. 725-732
Author(s):  
R. S. Davtyan
Keyword(s):  
Orthogonal Series ◽  
Partial Sums

On a Problem of Littlewood

1996 ◽  
Vol 3 (2) ◽  
pp. 121-132
Author(s):  
M. Khazaradze
Keyword(s):  
Fourier Series ◽  
Trigonometric Series ◽  
Orthogonal Series ◽  
Orthonormal System ◽  
Partial Sums

Abstract The theorem on the tending to zero of coefficients of a trigonometric series is proved when the L 1-norms of partial sums of this series are bounded. It is shown that the analog of Helson's theorem does not hold for orthogonal series with respect to the bounded orthonormal system. Two facts are given that are similar toWeis' theorem on the existence of a trigonometric series which is not a Fourier series and whose L 1-norms of partial sums are bounded.

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