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- W3100187951 abstract "Abstract Let β (1,2) be a Pisot number and let H β denote Garsia’s entropy for the Bernoulli convolution associated with β . Garsia, in 1963, showed that H β <1 for any Pisot β . For the Pisot numbers which satisfy x m = x m −1 + x m −2 + + x +1 (with m ≥2), Garsia’s entropy has been evaluated with high precision by Alexander and Zagier for m =2 and later by Grabner, Kirschenhofer and Tichy for m ≥3, and it proves to be close to 1. No other numerical values for H β are known. In the present paper we show that H β >0.81 for all Pisot β , and improve this lower bound for certain ranges of β . Our method is computational in nature." @default.
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- W3100187951 date "2010-04-22" @default.
- W3100187951 modified "2023-09-25" @default.
- W3100187951 title "A lower bound for Garsia’s entropy for certain Bernoulli convolutions" @default.
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- W3100187951 doi "https://doi.org/10.1112/s1461157008000430" @default.
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