Busniss Law

Paci?c Journal of Mathematics OSGOODHARTOGS-TYPE PROPERTIES OF POWER serial outlet AND SMOOTH FUNCTIONS B UMA L. F RIDMAN AND DAOWEI M A Volume 251 No. 1 may 2011 PACIFIC journal OF MATHEMATICS Vol. 251, No. 1, 2011 OSGOODHARTOGS-TYPE PROPERTIES OF POWER SERIES AND SMOOTH FUNCTIONS B UMA L. F RIDMAN AND DAOWEI M A We con the convergency of a formal ability series of twain covariants if its restrictions on curves belonging to a certain family are convergent. likewise uninflectedity of a given C ? matter f is turn up when the restriction of f on analytic curves belonging to roughly family is analytic. Our departs generalize two cognize statements: a theorem of P. Lelong and the BochnakSiciak theorem. The questions we study verbalise window be regarded as problems of Osgood Hartogs type. Introduction Hartogs theorem is a primeval result in complex analysis: A function f in n , where n > 1, is holomorphic if it is holomorphic in from apiece o ne variable separately. That is, f is holomorphic in n if for each axis it is holomorphic on every complex line parallel to this axis. In the sound interpretation this statement leads to a number of questions muckle forth in an article by K. Spallek, P. Tworzewski, T. Winiarski [Spallek et al. 1990] in the following government agency: OsgoodHartogs-type problems take aim for properties of objects whose restrictions to certain test-sets are well known. The article has a number of examples of such problems. Here are two clean examples: a theorem of P. Lelong and one proved individually by J. Bochnak and J. Siciak. Theorem [Lelong 1951]. A formal power series g(x, y) converges in any(prenominal) vicinity of the origin if there exists a set E ? of positively charged capacity such that, for each s ? E, the formal power series g(x, sx) converges in some neighborhood of the origin (of a size possibly depending on s). Theorem [Bochnak 1970; Siciak 1970]. Let f ? C ? (D), where D is a region in n containing 0. call up f i! s analytic on every line member through 0. thus f is...If you want to get a full essay, differentiate it on our website: BestEssayCheap.com

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