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Morera theorems via microlocal analysis
Journal of Geometric Analysis, 1996More general Morera theorems state that, if \(y(c)= \int_c fdz=0\) for certain subclasses of closed curves in a region, then \(f\) is holomorphic in that region. The present paper shows Morera theorems for circles passing through the origin, for circles of arbitrary radius and arbitrary center, and for translates of a fixed closed convex curve.
Globevnik, Josip, Quinto, Eric Todd
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2003
Throughout the following each point (x, y) ∊ ℝ2 is identified with the complex number \( z = x + iy = \rho e^{i\phi } \left( {\rho = \left| z \right|, - \pi < \phi \leqslant \pi } \right) \). Then the group of Euclidean motions of the complex plane can be identified with M(2). Let Ω be a domain in ℂ and let Hol(Ω) be the following set of functions from
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Throughout the following each point (x, y) ∊ ℝ2 is identified with the complex number \( z = x + iy = \rho e^{i\phi } \left( {\rho = \left| z \right|, - \pi < \phi \leqslant \pi } \right) \). Then the group of Euclidean motions of the complex plane can be identified with M(2). Let Ω be a domain in ℂ and let Hol(Ω) be the following set of functions from
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Local boundary Morera theorems
Mathematische Zeitschrift, 2000The following boundary Morera theorem is known [\textit{J. Globevnik}, J. Geom. Anal. 3, No. 3, 269-277 (1993; Zbl 0785.32008)]: Let \(D\subset \mathbb{C}^N\), \(N\geq 2\) be a bounded open set with \(C^2\) boundary and \({\mathcal L}\) be an open connected set of affine complex hyperplanes in \(\mathbb{C}^N\) containing a hyperplane that misses ...
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One Boundary Version of Morera's Theorem
Siberian Mathematical Journal, 2001Summary: Let \(D\) be a bounded domain in \(\mathbb C^n\) (\(n>1\)) with a connected smooth boundary \(\partial D\) and let \(f\) be a continuous function on \(\partial D\). We consider conditions (generalizing those of the Hartogs--Bochner theorem) for holomorphic extendibility of \(f\) to \(D\).
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On a boundary morera theorem for the classical domains
Siberian Mathematical Journal, 1999The authors analyze a boundary version of Morera's theorem for classical domains. The starting point is Nagel and Rudin's result claiming that, if a function \(f\) is continuous on the boundary of a ball in \(\mathbb C^N\) and \[ \int_0^{2\pi}f(\psi(e^{i\varphi}, 0\dots, 0)) e^{i\varphi} d\varphi = 0 \] for all (holomorphic) automorphisms \(\psi\) of ...
Kosbergenov, S. +2 more
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An extremum problem related to Morera's theorem
Mathematical Notes, 1996The following extension of Morera's theorem has been proved by \textit{C. Berenstein} and \textit{R. Gay} [J. Anal. Math. 52 133-166 (1989; Zbl 0668.30037)]: Let \(T \subseteq B_r= \{z\in\mathbb{C}:| z|
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2010
Biografia scientifica, con l'elenco delle fonti d'archivio e delle fonti bibliografiche.
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Biografia scientifica, con l'elenco delle fonti d'archivio e delle fonti bibliografiche.
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Multidimensional Boundary Morera Theorems in Matrix Domains
Journal of Mathematical ScienceszbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Morera type theorems on the unit disc
Analysis Mathematica, 1994The paper under review deals with some theorems concerning the holomorphic functions in the unit disk that are vanishing on some circle integrals. Earlier, similar results were known only for the whole complex plane. As a result the author has solved Farkas' problem (see: \textit{L. Zalcman}, [Arch. Rat. Mech. Analysis 47, 237-254 (1972; Zbl 0251.30047)
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