I. Berkes

activity

20042026

most citedThe efficiency of the estimators of the parameters in GARCH processes

182 citations · 508 across the 28 of their papers we have counts for

collaborators

Showing 2012 · math.CAShow all

3 papers · 2 filters

math.CA2012★ 1 cited

On convergence and growth of sums $\sum c_{k} f (k x)$

Istvan Berkes

For a periodic function $f$ with bounded variation and integral zero on its period interval, we show that $\sum_{k = 1}^{\infty} c_{k}^{2} (lo g lo g k)^{γ} < \infty$ , $γ > 4$ implies the almost…

math.CA2012

On series $\sum c_{k} f (k x)$ and Khinchin's conjecture

Istvan Berkes, Michel Weber

We prove the optimality of a criterion of Koksma (1953) in Khinchin's conjecture, settling a long standing open problem in analysis. Using this result, we also give a near optimal…

math.CA2012★ 1 cited

On series of dilated functions

Istvan Berkes, Michel Weber

Given a periodic function $f$ , we study the almost everywhere and norm convergence of series $\sum_{k = 1}^{\infty} c_{k} f (k x)$ . As the classical theory shows, the behavior of such seri…

On convergence and growth of sums ∑ck​f(kx)

On series ∑ck​f(kx) and Khinchin's conjecture

On series of dilated functions

On convergence and growth of sums $\sum c_{k} f (k x)$

On series $\sum c_{k} f (k x)$ and Khinchin's conjecture