Journal of Advances in Mathematics and Computer Science

Weierstrass’s Global Division Theorem and Continuity of Linear Operators in H -spaces

Eugeny Smirnov

Yaroslavl State Pedagogical University, 150000, Yaroslavl, Respublikanskaya, 108, Russia.

*Author to whom correspondence should be addressed.

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Abstract

In the present article generalization of Weierstrass’s preparation theorem and the division theorem for germs of holomorphic functions at a point of ⁿ -dimensional complex space are considered. The author formulates the global theorem about division in terms of existence and continuity of the linear operator.

Keywords: Weierstrass’s global division theorem, closed graph theorem, holomorphic functions, H -space.

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