Certain estimates for intermediate derivatives on a quasismooth arc are proved and applied. For arcs of bounded slope, the corresponding results by Bang and Leont ev are generalized.
We prove a criterion of quasi-analyticity in a boundary point of a rather general domain (not necessarily convex and simply-connected) if in a vicinity of this point the domain is close in some sense to an angle or is comparable with it.
In terms of the noncompleteness of a system of exponentials, a criterion is established for the nontriviality of the Siddiqi class on an arc of bounded slope all chords of which have slope strictly smaller than one.
Interpolation sequences of the form
are investigated, and also the problem of when the system of exponentials
is nonspanning on the family of arbitrary rectifiable curves in the uniform norm.
In terms of the interpolation nodes (or equivalently, the exponents of the system of exponentials) a criterion for the interpolation problem to be solvable is established and the strong nonspanning property of
is proved. This significantly improves some known results, in particular, results due to Korevaar, Dixon and Berndtsson.
Bibliography: 23 titles.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.