Two extension theorems of Hartogs-Chirka type involving continuous multifunctions
نویسندگان
چکیده
منابع مشابه
Hartogs Type Extension Theorems
Let ∆ ⊆ C be the open unit disc and let Σ ⊆ ∆×∆ be a compact set such that K = Σ ∪ (∂∆×∆) is a connected set. It is a classical result by Hartogs that if Σ is an analytic variety over ∆ with the boundary in ∂∆×∆, then every function holomorphic in a connected neighbourhood of K extends holomorphically to a neighbourhood of ∆ × ∆. It is proved that the same conclusion holds if Σ is a ‘continuous...
متن کاملThe Role of Fourier Modes in Extension Theorems of Hartogs-chirka Type
We generalize Chirka’s theorem on the extension of functions holomorphic in a neighbourhood of Γ (F )∪ (∂D ×D) – where D is the open unit disc and Γ (F ) is the graph of a continuous D-valued function F – to the bidisc. We extend holomorphic functions by applying the Kontinuitätssatz to certain continuous families of analytic annuli, which is a procedure suited to configurations not covered by ...
متن کاملHahn-Banach extension theorems for multifunctions revisited
Several generalizations of the Hahn–Banach extension theorem to K-convex multifunctions were stated recently in the literature. In this note we provide an easy direct proof for the multifunction version of the Hahn–Banach–Kantorovich theorem and show that in a quite general situation it can be obtained from existing results. Then we derive the Yang extension theorem using a similar proof as wel...
متن کاملHartogs Type Theorems on Coverings of Strongly Pseudoconvex Manifolds
We prove an analog of the classical Hartogs extension theorem for certain (possibly unbounded) domains on coverings of strongly pseudoconvex manifolds. Our result is related to a problem posed in the paper of Gromov, Henkin and Shubin [GHS] on holomorphic L2 functions on coverings of pseudoconvex manifolds. Previously in [Br3] similar results were established for some domains on coverings of St...
متن کاملHartogs Type Theorems on Coverings of Stein Manifolds
We prove an analog of the classical Hartogs extension theorem for certain (possibly unbounded) domains on coverings of Stein manifolds.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2011
ISSN: 0026-2285
DOI: 10.1307/mmj/1320763054