scholarly journals A Density problem for Hardy spaces of almost periodic functions

1984 ◽  
Vol 29 (3) ◽  
pp. 315-327 ◽  
Author(s):  
Robyn Owens

We construct a counterexample, for p = 1, to the conjecture posed by Milaszevitch in 1970: is the space of functions which are analytic in the upper half plane and uniformly almost periodic in its closure dense in the Hardy space Hp (0 < p ∞) of analytic almost periodic functions?

Mathematika ◽  
1955 ◽  
Vol 2 (2) ◽  
pp. 128-131 ◽  
Author(s):  
J. D. Weston

2018 ◽  
Vol 14 (09) ◽  
pp. 2343-2368
Author(s):  
Giacomo Cherubini

We prove the existence of asymptotic moments and an estimate on the tails of the limiting distribution for a specific class of almost periodic functions. Then we introduce the hyperbolic circle problem, proving an estimate on the asymptotic variance of the remainder that improves a result of Chamizo. Applying the results of the first part we prove the existence of limiting distribution and asymptotic moments for three functions that are integrated versions of the remainder, and were considered originally (with due adaptations to our settings) by Wolfe, Phillips and Rudnick, and Hill and Parnovski.


Sign in / Sign up

Export Citation Format

Share Document