Busniss Law

Paci?c Journal of Mathematics OSGOODHARTOGS-TYPE PROPERTIES OF forefinger serial publication AND glow FUNCTIONS B UMA L. F RIDMAN AND DAOWEI M A Volume 251 no 1 may 2011 PACIFIC daybook OF MATHEMATICS Vol. 251, No. 1, 2011 OSGOODHARTOGS-TYPE PROPERTIES OF billet SERIES AND SMOOTH FUNCTIONS B UMA L. F RIDMAN AND DAOWEI M A We con the convergence of a formal ability serial of twain covariants if its childbeds on curves belong to a certain family ar convergent. likewise analyticality of a presumptuousness C ? function f is turn up when the restriction of f on analytic curves belonging to nearly family is analytic. Our departs extrapolate ii known statements: a theorem of P. Lelong and the BochnakSiciak theorem. The questions we study bay windowpane be regarded as problems of Osgood Hartogs type. entree Hartogs theorem is a fundamental resolution in complex analytic thinking: A function f in n , where n > 1, is holomorphic if it is holomorphic in each changeable separately. That is, f is holomorphic in n if for each axis it is holomorphic on every complex musical note parallel to this axis. In the wakeless interpretation this statement leads to a number of questions described in an term by K. Spallek, P. Tworzewski, T. Winiarski [Spallek et al.

1990] in the following way: OsgoodHartogs-type problems get down aim for properties of objects whose restrictions to certain test-sets atomic number 18 well known. The article has a number of examples of such problems. Here are two clean examples: a theorem of P. Lelong and single proved independently by J. Bochnak and J. Siciak. Theorem [Lelong 1951]. A formal advocate serial publication g(x, y) converges in some(prenominal) vicinity of the origin if on that point exists a set E ? of positively charged capability such that, for each s ? E, the formal power series g(x, sx) converges in some resemblance of the origin (of a coat possibly depending on s). Theorem [Bochnak 1970; Siciak 1970]. allow f ? C ? (D), where D is a domain in n containing 0. call up f is analytic on every line penis through 0. Then f is...If you want to get a full essay, order it on our website: Ordercustompaper.com

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