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A lower bound on the radius of analyticity of a power series in a real Banach space

Timothy Nguyen (2009)

Studia Mathematica

Let F be a power series centered at the origin in a real Banach space with radius of uniform convergence ϱ. We show that F is analytic in the open ball B of radius ϱ/√e, and furthermore, the Taylor series of F about any point a ∈ B converges uniformly within every closed ball centered at a contained in B.

A microlocal version of Cartan-Grauert's theorem

I. V. Maresin, A. G. Sergeev (1998)

Annales Polonici Mathematici

Tuboids are tube-like domains which have a totally real edge and look asymptotically near the edge as a local tube over a convex cone. For such domains we state an analogue of Cartan’s theorem on the holomorphic convexity of totally real domains in ℝ n ⊂ ℂ n .

A natural localization of Hardy spaces in several complex variables

Mihai Putinar, Roland Wolff (1997)

Annales Polonici Mathematici

Let H²(bΩ) be the Hardy space of a bounded weakly pseudoconvex domain in ℂ n . The natural resolution of this space, provided by the tangential Cauchy-Riemann complex, is used to show that H²(bΩ) has the important localization property known as Bishop’s property (β). The paper is accompanied by some applications, previously known only for Bergman spaces.

A new characterization of the analytic surfaces in ℂ 3 that satisfy the local Phragmén-Lindelöf condition

Rüdiger W. Braun, Reinhold Meise, B. A. Taylor (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove that an analytic surface V in a neighborhood of the origin in ℂ 3 satisfies the local Phragmén-Lindelöf condition PL loc at the origin if and only if V satisfies the following two conditions: (1) V is nearly hyperbolic; (2) for each real simple curve γ in ℝ 3 and each d ≥ 1 , the (algebraic) limit variety T γ , d V satisfies the strong Phragmén-Lindelöf condition. These conditions are also necessary for any pure k -dimensional analytic variety V to satisify PL loc .

A new class of almost complex structures on tangent bundle of a Riemannian manifold

Amir Baghban, Esmaeil Abedi (2018)

Communications in Mathematics

In this paper, the standard almost complex structure on the tangent bunle of a Riemannian manifold will be generalized. We will generalize the standard one to the new ones such that the induced ( 0 , 2 ) -tensor on the tangent bundle using these structures and Liouville 1 -form will be a Riemannian metric. Moreover, under the integrability condition, the curvature operator of the base manifold will be classified.

A new class of pluripolar sets

Nguyen Quang Dieu, Tang Van Long (2007)

Annales Polonici Mathematici

Let D be a domain in ℂⁿ. We introduce a class of pluripolar sets in D which is essentially contained in the class of complete pluripolar sets. An application of this new class to the problem of approximation of holomorphic functions is also given.

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