Impossibility of the Carleman approximation of functions continuous on the unit circle by the boundary values of functions analytic and uniformly continuous on the unit disk
✍ Scribed by V. P. Khavin
- Publisher
- Springer US
- Year
- 1974
- Tongue
- English
- Weight
- 440 KB
- Volume
- 2
- Category
- Article
- ISSN
- 1573-8795
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📜 SIMILAR VOLUMES
## Abstract It is shown that the following conditions are equivalent for the generalized Schur class functions at a boundary point __t__~0~ ∈ 𝕋: 1) Carathéodory–Julia type condition of order __n__; 2) agreeing of asymptotics of the original function from inside and of its continuation by reflection
## Abstract Let __D__ be a unit disk and__M__ be an open arc of the unit circle whose Lebesgue measure satisfies 0 < __l__ (__M__) < 2__π__. Our first result characterizes the restriction of the holomorphic functions __f__ ∈ ℋ︁(__D__), which are in the Hardy class ℋ︁^1^ near the arc__M__ and are de