Weierstrass’s Global Division Theorem and Continuity of Linear Operators in H-spaces | Chapter 01 | Advances in Mathematics and Computer Science Vol. 2
We
introduce here new
concepts of functional
analysis: Hausdorff spectrum
and Hausdorff limit or
H-limit of Hausdorff spectrum
of locally convex
spaces. Author has
introduced this concepts
in 2002 but
progress in different areas of mathematics
(algebraic geometry, differential equations, category theory, ets) defined the
need to expand fundamental
concepts. Particular cases
of regular H-limit
are projective and inductive
limits of separated locally
convex spaces. The
class of H spaces
contains Fréchet spaces
and is stable
under the operations of forming countable
inductive and projective limits, closed subspaces and factor-spaces. Besides, for
H-space the strengthened variant of the closed graph theorem holds true. 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.
Author(s) Details
Eugeny Smirnov
Yaroslavl State Pedagogical
University, 150000, Yaroslavl, Respublikanskaya, 108/1, Russia.
View Volume: https://doi.org/10.9734/bpi/amacs/v2
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