Approximation of periodic functions by trigonometric polynomials in the mean

1974 ◽  
Vol 16 (1) ◽  
pp. 592-599
Author(s):  
V. P. Motornyi
Keyword(s):  
Trigonometric Polynomials ◽  
Periodic Functions ◽  
The Mean ◽  
Approximation Of Periodic Functions

scholarly journals Distribution of Small Values of Bohr Almost Periodic Functions with Bounded Spectrum

2019 ◽  
pp. 571-578
Author(s):  
Wayne M. Lawton
Keyword(s):  
Periodic Function ◽  
Riemann Hypothesis ◽  
Mahler Measure ◽  
Trigonometric Polynomials ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Periodic Functions ◽  
The Mean ◽  
Relationship Of ◽  
The Relationship

For f a nonzero Bohr almost periodic function on R with a bounded spectrum we proved there exist Cf > 0 and integer n > 0 such that for every u > 0 the mean measure of the set f x : jf(x)j < u g is less than Cf u1=n: For trigonometric polynomials with n + 1 frequencies we showed that Cf can be chosen to depend only on n and the modulus of the largest coefficient of f: We showed this bound implies that the Mahler measure M(h); of the lift h of f to a compactification G of R; is positive and discussed the relationship of Mahler measure to the Riemann Hypothesis

Approximation of periodic functions by Fourier sums in the mean

1986 ◽  
Vol 38 (2) ◽  
pp. 180-185 ◽  
Author(s):  
A. I. Stepanets ◽  
A. K. Novikova
Keyword(s):  
Periodic Functions ◽  
Fourier Sums ◽  
The Mean ◽  
Approximation Of Periodic Functions
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