Functions with the One-dimensional Holomorphic Extension Property
نویسندگان
چکیده
منابع مشابه
Contact Geometry of One Dimensional Holomorphic Foliations
ABSTRACT. Let V be a real hypersurface of class Ck, k ≥ 3, in a complex manifold M of complex dimension n + 1, HT (V ) the holomorphic tangent bundle to V giving the induced CR structure on V . Let θ be a contact form for (V,HT (V )), ξ0 the Reeb vector field determined by θ and assume that ξ0 is of class Ck. In this paper we prove the following theorem (cf. Theorem 4.1): if the integral curves...
متن کاملHolomorphic Extension Associated with Fourier–legendre Expansions
In this article we prove that if the coefficients of a Fourier–Legendre expansion satisfy a suitable Hausdorff–type condition, then the series converges to a function which admits a holomorphic extension to a cut–plane. Furthermore, we prove that a Laplace–type (Laplace composed with Radon) transform of the function describing the jump across the cut is the unique Carlsonian interpolation of th...
متن کاملSeparate Holomorphic Extension along Lines and Holomorphic Extension from the Sphere to the Ball
We give positive answer to a conjecture by Agranovsky in [1]. A continuous function on the sphere which has separate holomorphic extension along the complex lines which pass through three non-aligned interior points, is the trace of a holomorphic function in the ball. MSC: 32F10, 32F20, 32N15, 32T25
متن کاملTopological Pressure for One-dimensional Holomorphic Dynamical Systems
For a class of one-dimensional holomorphic maps f of the Riemann sphere we prove that for a wide class of potentials φ the topological pressure is entirely determined by the values of φ on the repelling periodic points of f . This is a version of a classical result of Bowen for hyperbolic diffeomorphisms in the holomorphic non-uniformly hyperbolic setting.
متن کاملFixed Point Theorems for Infinite Dimensional Holomorphic Functions
This talk discusses conditions on the numerical range of a holomorphic function defined on a bounded convex domain in a complex Banach space that imply that the function has a unique fixed point. In particular, extensions of the Earle-Hamilton Theorem are given for such domains. The theorems are applied to obtain a quantitative version of the inverse function theorem for holomorphic functions a...
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: Journal of Siberian Federal University. Mathematics & Physics
سال: 2019
ISSN: 2313-6022,1997-1397
DOI: 10.17516/1997-1397-2019-12-4-439-443