Let U be an open convex set in a Banach space E, F another Banach space. We consider the space H(U,F) of all F-valued holomorphic functions of bounded type in U possesing an asymptotic expansion in the origin. We study classes of asymptotic approximations such that two functions in the same class with an identical asymptotic expansion must coincide. In this paper, we characterize the functions belonging to some of these classes which are optimal approximations of a given series.
Let U be an open convex subset of Cn, n belonging to N, such that the set of all polinomies is dense in the space of all holomorphic and complex functions on U, (H(U), t0), where t0 is the open-compact topology.
We endow the space HK(U) of all holomorphic functions on U that have asymptotic expansion at the origin with a metric and we study a particular compact subset of HK(U).
This work deals with the study of the bounds of the asymptotic expansions of complex functions in a normed space. Some inequalities are obtained similar to the Gorny-Cartan for the bounds of asymptotic expansions in an angle of the complex space.
We define the radius of the inscribed and circumscribed circumferences in a triangle located in a real normed space and we obtain new characterizations of inner product spaces.
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