... determined by the following data:(i) the intervals (Ik)0≤k≤N/n1,(ii) the restriction of C to the union of the Iks,(iii) the values of C outside the Iks.Let us count in each case the number ... accordancewith the notation of the previous sections, we denote Ωi= B(Pi, ε/2).ENTROPY AND THE LOCALIZATION OF EIGENFUNCTIONS 449• Ai2= Aiexcept on a set of measure of order hκ.• For i = ... θ), n)-cover of Σ}, the minimal cardinality of an (h, (1 −θ), n)-cover of Σ.450 NALINI ANANTHARAMANRemember the notation: for C = [α0, . . . , αn−1] ∈ Σn,ˆChstands for the operatorˆCh=...