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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. LOMI, 1979 Volume 92, Pages 203–219 (Mi znsl3198)

Reconstruction of functions with the given modulus of continuity

A. A. Moisejev


Abstract: Let $\mu$ be a measure on $[a,b],C_{\omega,\mu}$ the class of all functions $f$ whose continuity modulus does not exceed the given function $\omega$ and such that $\int_a^bf\,d\mu=0$. The problem of eatimatinq $\operatorname{diam}C_{\omega,\mu}$ (in the space $C([a,b])$) is reduced to an equilibrium problem for the “potential” $\int\omega(|x-t|)\,d\mu(t)$.

UDC: 513.881



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