English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

derivation at p on R(X) if and only if, for all/ in R0(X), | f'(p) | ^ Mll/H for some constant M (||/||=sup{|/(2)|:Z£A}). Recently Hallstrom [2], using the techniques of Melnikov [3], has given a very nice characterization, expressed in terms of analytic capacity, describing when points in R(X) admit bounded point derivations. He also discussed the notion of point derivations of higher orders on R(X). For a positive integer k, a bounded point derivation of order k on R(X) at p is said to exist if there is a constant Af such that, for all/ in A0(A), |/«>0) I gMll/ll, where f(k)(p) denotes the &th derivative of/at p. Hallstrom extended his characterization for bounded point derivations of order 1 to include those of order k. In this note we obtain a similar characterization in terms of representing measures. That is, we show there exist bounded point derivations on R(X) of order k at a point p if and only if p has (complex) representing measures of a certain type. By a measure on X we mean a finite complex Baire measure on X. If p is a measure, |p| denotes its total variation. We call p a (complex) representing measure for a point p in A if

Bounded point derivations and representing measures on 𝑅(𝑋)