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.