Open Access
July, 2014 Resolvent estimates on symmetric spaces of noncompact type
J. Math. Soc. Japan 66(3): 895-926 (July, 2014). DOI: 10.2969/jmsj/06630895


In this article we prove resolvent estimates for the Laplace-Beltrami operator or more general elliptic Fourier multipliers on symmetric spaces of noncompact type. Then the Kato theory implies time-global smoothing estimates for corresponding dispersive equations, especially the Schrödinger evolution equation. For low-frequency estimates, a pseudo-dimension appears as an upper bound of the order of elliptic Fourier multipliers. A key of the proof is to show a weighted $L^{2}$-continuity of the modified Radon transform and fractional integral operators.


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Koichi KAIZUKA. "Resolvent estimates on symmetric spaces of noncompact type." J. Math. Soc. Japan 66 (3) 895 - 926, July, 2014.


Published: July, 2014
First available in Project Euclid: 24 July 2014

zbMATH: 1301.47045
MathSciNet: MR3238321
Digital Object Identifier: 10.2969/jmsj/06630895

Primary: 47A10
Secondary: 35B65 , 43A85

Keywords: Dispersive Equation , limiting absorption principle , resolvent , Smoothing effect , Symmetric space

Rights: Copyright © 2014 Mathematical Society of Japan

Vol.66 • No. 3 • July, 2014
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