Image of under the Hermite Semigroup

R. Radha and D. Venku Naidu

International Journal of Mathematics and Mathematical Sciences, 2008, vol. 2008, 1-13

Abstract:

It is shown that the Hermite (polynomial) semigroup maps into the space of holomorphic functions in for each , where is the Gaussian measure, is a scaled version of Gaussian measure with if and if with . Conversely if is a holomorphic function which is in a “slightly†smaller space, namely , then it is shown that there is a function such that . However, a single necessary and sufficient condition is obtained for the image of under , . Further it is shown that if is a holomorphic function such that or , then there exists a function such that , where and .

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:287218

DOI: 10.1155/2008/287218

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