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Image of Lp(ℝn) under the Hermite Semigroup
Joint Authors
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2008, Issue 2008 (31 Dec. 2008), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-02-26
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
It is shown that the Hermite (polynomial) semigroup {e−tℍ:t>0} maps Lp(ℝn,ρ) into the space of holomorphic functions in Lr(ℂn,Vt,p/2(r+ϵ)/2) for each ϵ>0, where ρ is the Gaussian measure, Vt,p/2(r+ϵ)/2 is a scaled version of Gaussian measure with r=p if 1
Conversely if F is a holomorphic function which is in a “slightly” smaller space, namely Lr(ℂn,Vt,p/2r/2), then it is shown that there is a function f∈Lp(ℝn,ρ) such that e−tℍf=F.
However, a single necessary and sufficient condition is obtained for the image of L2(ℝn,ρp/2) under e−tℍ, 1
Further it is shown that if F is a holomorphic function such that F∈L1(ℂn,Vt,p/21/2) or F∈Lm1,p(ℝ2n), then there exists a function f∈Lp(ℝn,ρ) such that e−tℍf=F, where m(x,y)=e−x2/(p−1)e4t+1e−y2/e4t−1 and 1
American Psychological Association (APA)
Radha, R.& Naidu, D. Venku. 2009. Image of Lp(ℝn) under the Hermite Semigroup. International Journal of Mathematics and Mathematical Sciences،Vol. 2008, no. 2008, pp.1-13.
https://search.emarefa.net/detail/BIM-460545
Modern Language Association (MLA)
Radha, R.& Naidu, D. Venku. Image of Lp(ℝn) under the Hermite Semigroup. International Journal of Mathematics and Mathematical Sciences No. 2008 (2008), pp.1-13.
https://search.emarefa.net/detail/BIM-460545
American Medical Association (AMA)
Radha, R.& Naidu, D. Venku. Image of Lp(ℝn) under the Hermite Semigroup. International Journal of Mathematics and Mathematical Sciences. 2009. Vol. 2008, no. 2008, pp.1-13.
https://search.emarefa.net/detail/BIM-460545
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-460545