Criteria for $ C^m$-approximability by bianalytic functions on planar compact setsстатья
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Аннотация:Abstract. The paper puts forward criteria for approximability by
bianalytic functions in the norms of the Whitney-type spaces Cm on
planar compact sets with m ∈ (0, 2). These results, which are analogues
of Vitushkin’s well-known criteria for uniform rational approximation,
together with results of O’Farrell and Verdera (the case m > 2) and Mazalov
(the case m = 0), provide a complete set of criteria for approximability by
bianalytic functions for all m > 0. These conditions for approximability
are obtained for both individual functions and (as corollaries) for classes
of functions, using the terminology of geometric measure theory.
Bibliography: 21 titles.