Singularities in the Distribution of the Increments of a Smooth Function.

Abstract

Let F(t), 0 < or = t < or = 1, be a real function with two continuous derivatives such that <F''=F=0> is empty. Then B yields meas. <(s,t): F(s)-F(t) is a member of B> is absolutely continuous; its density is continuous on IR/<B sub 1>, <B sub i> identical with <y: Y=F(t sub 1)-F(t sub 2), F'(t sub 1) = F'(t sub 2) = 0, F''(t sub 1), F''(t sub 2) > 0 >, and has a logarithmic singularity at each B sub i. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1977
Accession Number
ADA045124

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  • Donald Geman

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  • University of North Carolina at Chapel Hill

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  • Materials and Manufacturing Processes

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