GENERALIZED ANALYTIC FUNCTIONS ON THE COUNTABLE PRODUCT AND DIRECT SUM OF THE COMPLEX NUMBERS
2001 ◽
Vol 04
(04)
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pp. 559-567
Keyword(s):
A classical result states that, in n variables, the space of the entire functionals can be identified with the space of exponential type functions via the Fourier–Borel transform. Thus, in this way the spaces of the entire and exponential type functions can be put in duality, the Martineau duality. We give a proof that the entire functionals, on the countable direct product and direct sum of the field of complex numbers, can be identified with exponential type functions in the same way. In other words, we show that the infinite dimensional Fourier–Borel transform defines Martineau dualities analogous to the finite dimensional case.
2015 ◽
Vol 27
(04)
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pp. 1550011
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2004 ◽
Vol 2
(3)
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pp. 253-265
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1976 ◽
Vol 28
(1)
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pp. 174-180
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1977 ◽
Vol 29
(4)
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pp. 696-700
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2005 ◽
Vol 77
(4)
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pp. 589-594
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1995 ◽
Vol 38
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pp. 63-76
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1968 ◽
Vol 20
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pp. 344-361
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2012 ◽
Vol 2013
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pp. 1-48
2005 ◽
Vol 08
(03)
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pp. 497-504
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