Holomorphic functions with distinguished properties on infinite dimensional spaces
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Abstract In this paper, we develop a method to construct holomorphic functions that exist only on infinite dimensional spaces. The following types of holomorphic functions f:U→ℂ on some open subsets U of an infinite dimensional complex Banach space are constructed: (1) f is bounded holomorphic on U and is continuously, but not uniformly continuously extended to U¯; (2) f is continuous on U¯ and holomorphic of bounded type on U, but f is unbounded on U; (3) f is holomorphic of bounded type on U and f cannot be continuously extended to U¯. The technique we develop is powerful enough to provide, in the cases (2) and (3) above, large algebraic structures formed by such functions (up to the zero function, of course).
2019 ◽
Vol 38
(3)
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pp. 133-140
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1994 ◽
Vol 49
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pp. 249-256
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1986 ◽
Vol 28
(2)
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pp. 193-198
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1993 ◽
Vol 36
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pp. 197-209
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2002 ◽
Vol 73
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pp. 115-126
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1979 ◽
Vol 31
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pp. 1339-1344
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