A law of the iterated logarithm for general lacunary series

• Autorzy: Charles N. Moore , Xiaojing Zhang
• Języki publikacji: EN

Abstrakty

EN

We prove a law of the iterated logarithm for sums of the form $∑_{k=1}^{N} a_{k}f(n_{k}x)$ where the $n_{k}$ satisfy a Hadamard gap condition. Here we assume that f is a Dini continuous function on ℝⁿ which has the property that for every cube Q of sidelength 1 with corners in the lattice ℤⁿ, f vanishes on ∂Q and has mean value zero on Q.

Kategorie tematyczne

• 42A55: Lacunary series of trigonometric and other functions; Riesz products
• 60F15: Strong theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 126
• Numer: 1
• Strony: 95-103

Daty

wydano

2012

Twórcy

autor

Charles N. Moore

• Department of Mathematics, Kansas State University, Manhattan, KS 66506, U.S.A.

autor

Xiaojing Zhang

• Department of Mathematics, Kansas State University, Manhattan, KS 66506, U.S.A.

Identyfikatory

DOI

10.4064/cm126-1-6