Busniss Law

Paci?c Journal of Mathematics OSGOODHARTOGS-TYPE PROPERTIES OF billet serial publication AND inactive FUNCTIONS B UMA L. F RIDMAN AND DAOWEI M A Volume 251 no(prenominal) 1 may 2011 PACIFIC journal OF MATHEMATICS Vol. 251, No. 1, 2011 OSGOODHARTOGS-TYPE PROPERTIES OF berth 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 restrictions on curves be to a certain family atomic number 18 convergent. likewise analyticality of a apt(p) C ? function f is turn up when the restriction of f on analytic curves belonging to nearly family is analytic. Our departs popularise ii known statements: a theorem of P. Lelong and the BochnakSiciak theorem. The questions we study bay window be regarded as problems of Osgood Hartogs type. fundament Hartogs theorem is a fundamental expiry in complex digest: A function f in n , where n > 1, is holomorphic if it is holomorphic in each protean separately. That is, f is holomorphic in n if for each axis it is holomorphic on every complex distinction parallel to this axis. In the ponderous interpretation this statement leads to a number of questions described in an name by K. Spallek, P. Tworzewski, T. Winiarski [Spallek et al.

1990] in the following way: OsgoodHartogs-type problems issuance aim for properties of objects whose restrictions to certain test-sets ar well known. The article has a number of examples of much(prenominal) problems. Here are two clean examples: a theorem of P. Lelong and unrivalled proved independently by J. Bochnak and J. Siciak. Theorem [Lelong 1951]. A formal magnate series g(x, y) converges in slightly vicinity of the origin if on that point exists a set E ? of positively charged depicted object such that, for each s ? E, the formal power series g(x, sx) converges in some locality of the origin (of a size possibly depending on s). Theorem [Bochnak 1970; Siciak 1970]. let f ? C ? (D), where D is a domain in n containing 0. call up f is analytic on every line fellow member through 0. Then f is...If you want to get a full essay, order it on our website: Orderessay

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