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Full-Text Articles in Analysis
Polynomial And Rational Convexity Of Submanifolds Of Euclidean Complex Space, Octavian Mitrea
Polynomial And Rational Convexity Of Submanifolds Of Euclidean Complex Space, Octavian Mitrea
Electronic Thesis and Dissertation Repository
The goal of this dissertation is to prove two results which are essentially independent, but which do connect to each other via their direct applications to approximation theory, symplectic geometry, topology and Banach algebras. First we show that every smooth totally real compact surface in complex Euclidean space of dimension 2 with finitely many isolated singular points of the open Whitney umbrella type is locally polynomially convex. The second result is a characterization of the rational convexity of a general class of totally real compact immersions in complex Euclidean space of dimension n..
On The Continuation Of The Hartogs Series With Holomorphic Coefficients, Takhir Tuychiev, Jurabay Tishabaev
On The Continuation Of The Hartogs Series With Holomorphic Coefficients, Takhir Tuychiev, Jurabay Tishabaev
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In this paper we consider the question of continuation of the sums of the Hartogs series that admit holomorphic continuation along a fixed direction with “thin” singularities, assuming only the holomorphic of the coefficients of the series and investigate the convergence region of such series. The results of the work develop a well-known result of A.Sadullaev and E.M.Chirka on the continuation of functions with polar singularities.