Wyniki wyszukiwania - Biblioteka Nauki

Nowa wersja platformy, zawierająca wyłącznie zasoby pełnotekstowe, jest już dostępna.
Przejdź na https://bibliotekanauki.pl

Ograniczanie wyników

Znaleziono wyników: 4

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

A version of the law of large numbers

100%

Fukuyama K.

Colloquium Mathematicum

2001

tom 90

nr 2

295-298

By the method of Rio [10], for a locally square integrable periodic function f, we prove $(f(μ₁^{t}x) +...+ f(μₙ^{t}x))/n → ∫_{0}^{1}f$ for almost every x and t > 0.

On a gap series of Mark Kac

100%

Fukuyama K.

Colloquium Mathematicum

1999

tom 81

nr 2

157-160

Mark Kac gave an example of a function f on the unit interval such that f cannot be written as f(t)=g(2t)-g(t) with an integrable function g, but the limiting variance of $n^{-1/2}\sum_{k=0}^{n-1} f(2^kt)$ vanishes. It is proved that there is no measurable g such that f(t)=g(2t)-g(t). It is also proved that there is a non-measurable g which satisfies this equality.

Recurrence for cosine series with bounded gaps

63%

Fukuyama K. , Neupane D.

Colloquium Mathematicum

2010

tom 121

nr 2

281-284

Ullrich, Grubb and Moore proved that a lacunary trigonometric series satisfying Hadamard's gap condition is recurrent a.e. We prove the existence of a recurrent trigonometric series with bounded gaps.

Optimal bound for the discrepancies of lacunary sequences

51%

Aistleitner C. , Fukuyama K. , Furuya Y.

Acta Arithmetica

2013

tom 158

nr 3

229-243

The law of the iterated logarithm for discrepancies of lacunary sequences is studied. An optimal bound is given under a very mild Diophantine type condition.