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Original Articles

On the Fourier transforms of self-similar measures

Pages 468-484 | Received 03 Dec 2014, Accepted 08 Jul 2015, Published online: 28 Aug 2015
 

Abstract

For the Fourier transform of a general (non-trivial) self-similar measure μ on the real line , we prove a large deviation estimate

2010 Mathematics Subject Classification:

Acknowledgements

This work was supported by JSPS KAKENHI, Grant Number 22340035.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. Actually we cannot apply the results in [Citation10] and [Citation11] directly because the function ψ has logarithmic singularities at x = ±π/2 and hence is not continuous. Still we can obtain the large deviation estimate stated here by approximating ψ by smooth functions from above. It seems reasonable to expect that the limit is exact and the inequality is actually an equality.

Additional information

Funding

This work was supported by JSPS KAKENHI [grant number 22340035].

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