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J. Aust. Math. Soc.
76 (2004), 235-246 | ||
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The exponential representation of holomorphic functions of uniformly bounded type
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| Abstract | ||
It is shown that if
 ,
 are Fréchet spaces,
 ,
 then  holds. Using this result we prove that a
Fréchet space  is nuclear and has the property
 if and only if every entire function on
 with values in a Fréchet space
 can be represented in the exponential form.
Moreover, it is also shown that if
 has a LAERS and
 then
 has a LAERS, where
 ,
 are nuclear Fréchet spaces,
 has an absolute basis, and conversely, if
 has a LAERS and
 then
 .
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