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Image of under the Hermite Semigroup

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  • R. Radha
  • D. Venku Naidu

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 .

Suggested Citation

  • R. Radha & D. Venku Naidu, 2008. "Image of under the Hermite Semigroup," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2008, pages 1-13, February.
    • Handle: RePEc:hin:jijmms:287218
    DOI: 10.1155/2008/287218
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