The Logarithmic Integral Converges
Divergence of a logarithmic integral is the principal sufficient condition of many forms of the UP. But in fact it coincides with the necessary condition. The logarithmic integral determines a border-line separating two realms, the one undividedly governed by the UP (and described in Chapter 2) and the other where the resistance to the UP is possible and non-zero pairs (f, f̂) are allowed whose elements are small simultaneously. This chapter is devoted to methods of construction (or at least to the existence proofs) of such pairs.
KeywordsCharacteristic Function Entire Function Tauberian Theorem Homogeneous Mass Logarithmic Potential
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