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An elementary proof of the decomposition of measures on the circle group

100%

Ohrysko P.

Colloquium Mathematicum

2015

tom 140

nr 1

1-4

We give an elementary proof for the case of the circle group of the theorem of O. Hatori and E. Sato, which states that every measure on a compact abelian group G can be decomposed into a sum of two measures with a natural spectrum and a discrete measure.

On the relationships between Fourier-Stieltjes coefficients and spectra of measures

63%

Ohrysko P., Wojciechowski M.

Studia Mathematica

2014

tom 221

nr 2

117-140

We construct examples of uncountable compact subsets of complex numbers with the property that any Borel measure on the circle group with Fourier coefficients taking values in this set has a natural spectrum. For measures with Fourier coefficients tending to 0 we construct an open set with this property. We also give an example of a singular measure whose spectrum is contained in our set.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Studia Mathematica

2 Ohrysko P.

1 Wojciechowski M.

1 2015

1 2014

Wyniki wyszukiwania

An elementary proof of the decomposition of measures on the circle group

On the relationships between Fourier-Stieltjes coefficients and spectra of measures