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Spectral multipliers of Laplace transform type for the Laguerre operator

Published online by Cambridge University Press:  17 April 2009

Emanuela Sasso
Emanuela Sasso
Affiliation:
Dipartimėnto di Matematica, Universita di Genova, via Dodecanesco 35, 16146 Geonva, Italy
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We shall work with the Laguerre measure on and the associated Laplacian ℒα, by means of which the Laguerre semigroup is defined. Our main result is a multiplier theorem, saying that a functions of ℒα which is of Laplace transform type defines an operator of weak type (1, 1) for the Laguerre measure. Our starting point is the well-known relationship between the Laguerre and Ornstein-Uhlenbeck semigroups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 2 , April 2004 , pp. 255 - 266
Copyright
Copyright © Australian Mathematical Society 2004

References

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