On the Hartogs-type series for harmonic functions on Hartogs domains in $ℝ^n × ℝ^m$, m ≥ 2
نویسندگان
چکیده
منابع مشابه
Lineally convex Hartogs domains
We study lineally convex domains of a special type, viz. Hartogs domains, and prove that such sets can be characterized by local conditions if they are smoothly bounded.
متن کاملHartogs 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 Equivalent Classical Metrics on the Cartan-hartogs Domains
In this paper we study the complete invariant metrics on CartanHartogs domains which are the special types of Hua domains. Firstly, we introduce a class of new complete invariant metrics on these domains, and prove that these metrics are equivalent to the Bergman metric. Secondly, the Ricci curvatures under these new metrics are bounded from above and below by the negative constants. Thirdly, w...
متن کاملOn D ∗ - Extension Property of the Hartogs Domains
A complex analytic space is said to have the D∗-extension property if and only if any holomorphic map from the punctured disk to the given space extends to a holomorphic map from the whole disk to the same space. A Hartogs domain H over the base X (a complex space) is a subset of X × C where all the fibers over X are disks centered at the origin, possibly of infinite radius. Denote by φ the fun...
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 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: Annales Polonici Mathematici
سال: 1999
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap-71-2-151-160