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Vietnam
Journal of Mathematics 37:2&3 (2009) 357-378
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Characterizations of the Linear Topological Invariants
and the Solutions to some Problems of Holomorphic Functions
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Thai Thuan Quang
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Abstract. The theory of holomorphic functions
between locally convex spaces having linear topological invariants has
attracted the attention of many researchers during the last thirty years.
This report is a survey about recent results of the following problems from
this theory:
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1. Locally bounded holomorphic functions,
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2. The regularity of spaces of germ of Fréchet-valued holomorphic
functions,
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3. Weakly holomorphic functions, δ- separately holomorphic
functions,
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4. σ(., W)-holomorphic functions and theorems of
Vitali-type,
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5. The exponential representation of holomorphic functions and absolute
representation system,
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6. Separately holomorphic functions,
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7. Holomorphic functions of uniformly bounded type on tensor products.
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2000 Mathematics Subject Classification: 32A10, 32B10,
46A04, 46E50, 46A63, 30B50.
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Keywords: Holomorphic functions, Holomorphic
functions of uniform type, Topological linear invariants, Exponential
representation.
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