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Journal of the London Mathematical Society 2002 66(3):691-709; doi:10.1112/S0024610702003563
© 2002 by London Mathematical Society
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© The London Mathematical Society

Oscillatory Multipliers Related to the Wave Equation on Noncompact Symmetric Spaces

Michael Cowling, S. Giulini and Stefano Meda

School of Mathematics, University of New South Wales UNSW Sydney, NSW 2052, Australia, m.cowling{at}unsw.edu.au
Dipartimento di Matematica, Università di Genova via Dodecaneso 35, 16146 Genova, Italy, giulini{at}dima.unige.it
Dipartimento di Statistica, Università di Milano-Bicocca via Bicocca degli Arcimboldi 8, 20126 Milano, Italy, stemed{at}mate.polimi.it

Received 16 June 2000. Revision received 1 February 2002.

This paper is devoted to the study of a family of oscillatory multipliers of the Laplace–Beltrami operator on symmetric spaces of the noncompact type. This family is related to the regularity (in space, for fixed time) of the solutions to the wave equation. Our method relies on estimates for the Poisson semigroup in complex time, which were obtained in our previous paper [6].


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