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James C. Robinson. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, U.K.. E-mail: [email protected]. Abstract. Takens' time delay ...
Nov 5, 2012 - 2 Department of Mathematics, University of Nuernberg-Erlanegen, 91058 Erlangen, Germany. â Dedicated to Karl Willy Wagner (1883â1953).
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May 12, 1999 - such that if { is a critical number of F (i.e. F({) = { > 0) and f 2 AVAR. { , then. A; f j= H ... WWW: http://mizar.org/JFM/Vol2/zf_refle.html. The articles ...
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ON DIRICHLET'S THEOREM AND INFINITE PRIMES. CARTER WAID. Abstract. It is shown that Dirichlet's theorem on primes in an arithmetic progression is ...
Hans Havlicek. May 21, 2013. Abstract. We establish a version of von Staudt's theorem on mappings which pre- ...... Shaker. Verlag, Aachen, 2005.
m E 911 that is omitted in 911, then there is an 91^ 911 that also omits p(x, m). Before proving Theorem 2.1, we shall have to avail ourselves of some pre-.
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radó's theorem for cr-functions - Semantic Scholar
JEAN PIERRE ROSAY AND EDGAR LEE STOUT. (Communicated by Irwin Kra). Abstract. We establish an analogue of a classical theorem of Radó for CR-.
proceedings of the american mathematical society Volume 106, Number 4, August 1989
RADÓ'S THEOREM FOR CR-FUNCTIONS JEAN PIERRE ROSAYAND EDGAR LEE STOUT (Communicated by Irwin Kra)
Abstract. We establish an analogue of a classical theorem of Radó for CRfunctions on certain hypersurfaces in CN .
I. INTRODUCTION
A well-known theorem of Radó states that a continuous function defined on an open set in C that is holomorphic on the complement of its zero set is holomorphic everywhere. The result is correct in C as well as in the plane. The usual proofs rely on properties of subharmonic functions [11, 14] or on methods of the theory of uniform algebras [3, 19]. Our purpose here is to obtain an analogue of Radó's theorem in case of CR-functions defined on hypersurfaces in C . Our analysis does not cover the case of completely general hypersurfaces; for our proof we need to impose conditions on the size of the set where the Levi form vanishes. We obtain two results, the first of which is as follows. Proposition 1. If X is a strictly pseudoconvex hypersurface of class W in an open set in C , and if u is a continuous function on Z the restriction of which to I\u~ (0) is a CR-function, then u is a CR-function on I.
It then follows that u extends locally to the pseudoconvex side of X as a holomorphic function. As usual, a CR-function on Z is defined to be a function that satisfies the tangential Cauchy-Riemann equations dbu = 0, which, in case that u merely continuous, means that
/ udbj}°°=\ > a sequence of holomorphic functions on C that satisfy \f.\As) = (s ,j maps U into cf\K, such that
dist(0j{e'e),K) > S, and such that 4>-(0) tends to some point p0 e K as k tends to infinity. If we set fj(zl,z2) = l/(z2 - cp]{zx)), then f. is a holomorphic function ^
_2
defined on a neighborhood of K n U . By the Oka-Weil theorem, f. can be approximated
