A morera type theorem in the strip
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In this paper, a continuous function in the closed infinite strip in complex plane is shown to be holomorphic in the open strip, where the restriction of f to every circle inscribed in the strip extends holomorphically inside the circle.Abstract:
We prove the following result. Let f be a continuous function in the closed infinite strip in complex plane. Suppose the restriction of f to every circle inscribed in the strip extends holomorphically inside the circle. Then f is holomorphic in the open strip.read more
Citations
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Analyticity on circles for rational and real-analytic functions of two real variables
Mark Agranovsky,Josip Globevnik +1 more
TL;DR: Conditions for rational and real-analytic functions of two real variables to be holomorphic are given in terms of holomorphic extendibility from families of circles as discussed by the authors, which is the same as the conditions for rational functions of real variables.
Journal ArticleDOI
Testing analyticity on circles
TL;DR: In this article, it was shown that if a continuous function on the union of the circles extends holomorphically into each circle, then the function is holomorphic in the interior of the union.
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Propagation of boundary CR foliations and Morera type theorems for manifolds with attached analytic discs
TL;DR: In this article, it was shown that for real-analytic functions and arbitrary generic realanalytic families of curves, the answer is "yes" if no point is surrounded by all curves from the family.
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Analog of a theorem of forelli for boundary values of holomorphic functions on the unit ball of ℂ n
TL;DR: In this paper, it was shown that for every complex line L passing through one of a or b, the restricted function has a holomorphic extention to the cross-section L∩Bn, where Bn is the unit ball of ℂn.
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Characterization of polyanalytic functions by meromorphic extensions from chains of circles
TL;DR: In this article, the discriminant set S of a C1-family of circles in the plane is defined as the closure of the set {c(t + r(t)w(t), t ∈ [0, 1]], where w = w(t] is the root of the quadratic equation c′(t )w2 + 2r′(T)w + c′ (t) = 0 with |w| < 1, if such a root exists.
References
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Book
Real Submanifolds in Complex Space and Their Mappings
TL;DR: In this paper, Holomorphic extension of submanifolds has been studied in the context of real-algebraic subvarieties, and the boundary values of Holomorphic functions in Wedges have been analyzed.
Book
CR Manifolds and the Tangential Cauchy-Riemann Complex
TL;DR: In this paper, the Tangential Cauchy Riemann complex is considered and the authors present a non-Imbeddable C8 Abstract CR Manifold and an analytical Disc Technique.
Journal ArticleDOI
A Property of the Functions and Distributions Annihilated by a Locally Integrable System of Complex Vector Fields
M. S. Baouendi,François Treves +1 more
TL;DR: In this article, the fundamental theorem of homogeneous equations is interpreted as follows: "the fibers of the classical solutions of the homogeneous equation can be approximated and constancy on the fibers".
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Pompeiu's problem on symmetric spaces
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Propagation of holomorphic extendability of CR functions
Nicholas Hanges,François Treves +1 more